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In the literature, implants with significant stiffness superior to the bone tissue are incompatible because they can provide bone resorption and consequent aseptic loosening of the implant, even so, they continue to be developed and with a high success rate. Therefore, in order to infer the real influence of the modulus of elasticity of dental implants on peri-implant biomechanics, this review was carried out to answer the question “What is the influence of the modulus of elasticity of dental implants on the distribution of stresses in the alveolar bone by the method of finite elements?”. This review followed the PRISMA guidelines and the personalized search strategy was applied to Embase, PubMed, Scopus, and Science Direct databases. The selection process occurred in 2 steps by 2 reviewers independently. Studies that evaluated the influence of the modulus of elasticity of dental implants on stress distribution by the finite element method were included, without time and language restrictions. The risk of bias analysis was performed by adapting a checklist of important parameters to be considered.

Introduction. Over the past decade, global demand for pressure vessels has increased significantly, specifically in such industries as aviation, space, chemical, and oil and gas. Being under the constant impact of high internal pressure, the walls of the tanks are under increased stress, which can cause their sudden destruction. To eliminate this probability and improve the strength characteristics, the tanks are made in the form of metal cylinders with an internal coating of composite material consisting of resin reinforced with carbon fibers. This article aimed at studying the effect of the angle of inclination of carbon fiber on cylindrical tanks and determining the maximum destructive pressure using the finite element method of ANSYS program. Materials and Methods. Using the ANSYS program, a finite element model of a tank was created. It has a central part, which is a metal cylinder with an internal coating of composite material consisting of polymer reinforced with carbon fibers. At the ends of the tank, spiral wound hemispheres were placed. In these studies, SHELL 99 was used to model the layered composite material. The Tsai-Wu theory was used to determine the pressure tank failure criterion. Results. The cylindrical tank model was calculated for two types of fiber winding paths: annular and spiral, at different angles of their inclination. The results of the pressure value analysis for different fiber inclination angles showed that, starting from the angle value of 0° and up to 45°, it increased, and then, up to the angle value of 65°, it began to decrease. The critical pressure value for a carbon fiber reinforced tank was 207 MPa, which was obtained at a fiber angle of 45 o . Discussion and Conclusion. Analysis of the studies showed that at a fiber inclination angle of 45 o , the value of the maximum stress turned out to be the smallest, and the maximum possible destructive pressure at the same angle was 207 MPa. It follows, that the optimal fiber orientation angle to provide safe operation of the high-pressure tank is  45 о , and the carbon fiber tank, calculated at the same fiber winding angle, has the maximum strength value.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

The Finite Element Methods was used to solve the nonlinear electron plasma equations for the System-Generated Electromagnetic Pulse boundary layer in one spatial dimension. These equations were solved in distance-velocity phase space using a rectangular finite element mesh. Linear approximations were used for both the trial and weight functions for each element. The advection terms in the Vlasov plasma equation were treated with the Heinrich upwinding technique. The time integration was performed using an explicit two-step Lax-Wendroff procedure. The system of algebraic equations were solved with a fully-packed Gauss-Seidel iteration scheme. A value of 2/3 for the upwinding parameter was found to provide the best compromise between dispersion of the pulse, and computer storage requirements. The savings in computer memory results in increased execution speed for the algorithm. Also, it is shown that the numerical scheme does not permit spurious pulse reflections from the edges of the mesh. Results for several test cases are presented. Comparisons are given which show favorable agreement for the finite element technique with other solution relationships.

This report describes progress made in research during the final year of a five-year study of numerical dynamical analysis of structures funded by an AFOSR Grant. The original proposal was JPL Proposal 51-641 dated 6-29-76, and the final year renewal was proposed on 12-18-80. The proposed work effort in the final year's work included the following Tasks: (1) development of a higher order rectangular plane stress/strain finite element, (2) development of a solid hexahedron finite dynamic element, (3) further refinement of the Associated Generalized Eigenproblem Solution Routine. (Author)

A normally incident Rayleigh wave may be used for the investigation of a general vertical boundary and the attenuation of a viscoelastic medium. Use of energy conservation and proper boundary conditions produce 2 N second order differential equations, N being the number of viscoelastic layers in the medium. The homogeneous part of the differential equations can be transformed into an eigenvalue problem by the use of finite element technique; the eigenvalue and eigenvectors of the eigenvalue problem are the wavenumbers and the displacement amplitudes of the viscoelastic layered medium. The real and imaginary parts of the wavenumber determine the phase velocity and the attenuation of the layered medium, respectively. Dispersion and the attenuation curves can be obtained by using different periods. The above wavenumbers can be used in the inhomogeneous differential equation; this equation contains the effect of the vertical boundary; solution of this equation determines the displacement at the vertical boundary.

A significant increase in pore water pressure during construction of earth dams may lead to the hydraulic fracture of dam body in pounding. Thus having sufficient information about generation pattern of excess pore water pressure inside the core is essential. In the present study, using finite element method in coupled analysis of earth dams, excess pore water pressure and displacement values are estimated during the construction of Daroongar dam by developed Fortran code, and the results were compared with instrumentation data. Finally the actual amounts of horizontal and vertical permeability coefficients were determined for the materials by regression analysis.

There are three versions of finite element method. The classical h-version achieves the accuracy by refining the mesh while using low degrees P of elements, p=1,2 usually. The p-version keep the mesh fixed and the accuracy is achieved by increasing the degree p. The h-p version properly combines both approaches. The h-p version is the new development of finite element method. It was first addressed by Babuska and Dorr ?4 . The further analysis and computation for two dimensional problems were made by Guo, Babuska where the exponential rate of convergence was proved. The one dimensional analysis was given by Guo Babuska. The improvement of the results for curvilinear boundary and curvilinear elements was made by Babuska, Guo. The problem with non-homogeneous Dirichlet data was studied by Babuska, Guo. The h-p version with elements for the problem of 2m order was discussed by Guo. The feedback and adaptive approach was developed by Guo, Babuska and Babuska, Rank. This paper is addressing some theoretical advances and presents numerical illustrations.

In this study, we describe the algebraic computations required to implement the stochastic finite element method for solving problems in which uncertainty is restricted to right hand side data coming from forcing functions or boundary conditions. We show that the solution can be represented in a compact outer product form which leads to efficiencies in both work and sorage, and we demonstrate that block iterative methods for algebraic systems with multiple right hand sides can be used to advantage to compute this solution. Finally, we examine the behavior of these statistical quantities in one setting derived from a model of acoustic scattering.

The theory of the computable a-posteriori error estimate for a finite element method is developed. Among other things, it is shown that the error estimate is very reliable and the ratio (called effectivity index) between the estimator and the true error approaches one. Numerical examples computed by program FEARS (Finite Element Adaptive Research Solver) of the University of Maryland, illustrate the effectivity and reliability of the estimators. (Author)

The theory of the computable a-posteriori error estimate for a finite element method is developed. Among other things, it is shown that the error estimate is very reliable and the ratio (called effectivity index) between the estimator and the true error approaches one. Numerical examples computed by program FEARS (Finite Element Adaptive Research Solver) of the University of Maryland, illustrate the effectivity and reliability of the estimators. (Author)

We present a minimum-residual finite element method for convection-diffusion problems in a higher order, adaptive, continuous Galerkin setting. The method borrows concepts from both the Discontinuous Petrov-Galerkin (DPG) method by Demkowicz and Gopalakrishnan [1] and the method of variational stabilization by Dahmen et al. [2], and it can also be interpreted as a variational multiscale method in which the fine-scales are defined through a dual-orthogonality condition. A key ingredient in the method is the proper choice of norm used to measure the residual, and we present two alternatives which are observed to be robust in both convection and diffusion-dominated regimes. Numerically obtained convergence rates are given in 2D, and benchmark numerical examples in all space dimensions are shown to illustrate the behavior of the method.

Scattering from a one-dimensional rough surface with Gaussian roughness spectrum is analyzed using a finite element formulation. The method is applied to Monte Carlo simulations satisfying Neumann boundary conditions. Finite element results are compared with results obtained by solving an integral equation. Convergence of the method is verified by varying the number of nodal points in the first order, triangular mesh. Results are in excellent agreement with tapered wave integral equation solutions for large surface length after averaging over realizations. Finite element advantages in time and memory storage are presented for the examples discussed. Comparisons with the Kirchoff approximation and small perturbation theory within their respective regions of validity are also presented. Additionally, analysis of the effects of decreasing surface length on incoherent scattering results of the finite element method is accomplished to investigate the method's likely advantages for large-scale scattering problems. Numerical results of scattering are represented in terms of the normalized bistatic scattering cross section.

The finite element method is very powerful and flexible to model complex geometries with computers, because the region of interest can be subdivided into finite elements accurately. The advantages and drawbacks of the finite-element method will be the focus of the rudimentary investigation presented in this report. Especially, the requirements in terms of computational effort and computer memory storage will be investigated with respect to Nuclear ElectroMagnetic Pulse (NEMP) research requirements, i.e., with configurations frequently found in NEMP research such as coupling and interaction studies, simulator design and sensor design. Such configurations are often three dimensional and of intricate geometry. It is found that with present day computer capability it is not yet possible to solve real-life three dimensional geometries with the finite-element method, because of the memory requirements needed to store the resulting system of equations. Two dimensional geometries can at present be solved with the finite-element method, but the usefulness of two dimensional geometries for NEMP research purposes is questionable.

The paper analyzes the divergence stability of the p-version of the finite element method with the applications to the Stokes problem and elasticity problem with nearly uncompressible material. Many problems in continuum mechanics involve an incompressibility condition, usually in the form of a divergence constraint. The numerical discretization of such a constraint presents some interesting problems with regard to stability. As an important example we consider the two dimensional Stokes equations. The lack of divergence stability affects the accuracy of the pressure approximation much more drastically, and a certain postprocessing (filtering) of the pressures may be necessary as p approaches infinity. (jhd)

The theory of the computable a-posteriori error estimate for a finite element method is developed. Among other things, it is shown that the error estimate is very reliable and the ratio (called effectivity index) between the estimator and the true error approaches one. Numerical examples computed by program FEARS (Finite Element Adaptive Research Solver) of the University of Maryland, illustrate the effectivity and reliability of the estimators. (Author)

This research is directed toward the numerical analysis of large, three dimensional, nonlinear dynamic problems in structural and solid mechanics. Such problems include those exhibiting large deformations, displacements, or rotations, those requiring finite strain plasticity material models that couple geometric and material nonlinearities, and those demanding detailed geometric modeling. A finite element code was developed, designed around the 3D isoparametric family of elements, and using a Total Lagrangian formulation and implicit integration of the global equations of motion. The research was conducted using the Alliant FX/8 and Convex C240 supercomputers. The research focuses on four main areas: Development of element computation algorithms that exploit the inherent opportunities for concurrency and vectorization present in the finite element method; Comparison of the preconditioned conjugate gradient method to a representative direct solver; Investigation of various nonlinear solution algorithms, such as modified Newton-Raphson, secant-Newton, and nonlinear preconditioned conjugate gradient; and, Discovery of an accurate, robust finite strain plasticity material model.

This report describes the development of a finite-element model for analyzing sheet-metal forming processes. Materials are assumed to be rigid-plastic with the view that the usefulness of an analysis method depends largely upon solution accuracy and computation efficiency. First, the variational formulation applicable to sheet-metal forming is described by considering solution uniqueness and the effect of geometry change involved in the following processes. From this variational formulation, a finite-element process model based on the membrane theory is developed. Then, three basic sheet-metal forming processes, namely, the bulging of a sheet subject to hydrostatic pressure, the stretching of a sheet with a hemispherical head punch, and deep drawing of a sheet with a hemispherical head punch, are solved. The solutions arrived at by the rigid-plastic, finite-element method are compared with existing numerical solutions and the experimental data. The agreement is generally excellent and it is concluded that the rigid-plastic, finite-element method is efficient for analyzing sheet-metal forming problems with reasonable accuracy. (Author)

The hybrid stress method has demonstrated many improvements over conventional displacement-based elements. A main detraction from the method, however, has been the higher computational cost in forming element stiffness coefficients due to matrix inversions and manipulations as required by the technique. By utilizing special transformations of initially assumed stress fields, a spanning set of orthonormalized stress modes can be generated which simplify the matrix equations and allow explicit expressions for element stiffness coefficients to be derived. The developed methodology is demonstrated using several selected 2-D quadrilateral and 3-D hexahedral elements. Finite element analysis

Two primary thrusts have been put forth in our recent work on the quasicontinuum method. First, the method was generalized so as to allow for the treatment of materials involving multiple grains. A second key development has been the extension of the method to three dimensions. These developments have made it possible to examine the detailed microscopic mechanisms that accompany defect interactions. In particular, we have examined dislocation-grain boundary interactions, crack-grain boundary interactions and dislocation-dislocation interactions.

The use of object-oriented programming techniques in development of parallel, finite element analysis software enhances software reused and makes application development more efficient. In this report, an object-oriented programming framework for developing parallel finite element software is described. All required steps, from date file parsing and equation solving to post processing and graphical user interfaces, are discussed. After development of the framework, a sample parallel finite element code, namely COMPOSE, is extracted from its original functional programming paradigm and implemented in the new object-oriented programming framework. Besides ease of development, the use of generic visualization and interface tools for software using the framework speeds delivery of research codes to end users.

In this paper, we address the problem of the existence of superconvergence points of approximate solutions, obtained from the Generalized Finite Element Method (GFEM), of a Neumann elliptic boundary value problem. GFEM is a Galerkin method that uses non-polynomial shape functions. In particular, we show that the superconvergence points for the gradient of the approximate are zeros of certain systems of non-linear equations that do not depend on the solution of the boundary value problem. For approximate solutions with second derivatives, we have also characterized the superconvergence points of the second derivatives of the approximate solution as the roots of certain systems of non-linear equations. We note that it is easy to construct smooth generalized finite element approximation.

Finite element analysis has been used as a design to ol for many years, with structural reliability being ensured through use of a liberal factor of safety. Unfortunately, the safety factor is a blanket insurance against all hazards, and a designer has no way to optimize a structure against any particular hazard. This is particularly troublesome in the fields of aero/astro design, where every bit of mass must serve to maximum utility. The method of Stochastic Finite Element Analysis allows a designer to model any loading or hazard condition as closely to reality as desired by using an appropriate probability distribution function. Through a Monte Carlo simulation, the finite element model is subject to the probability functions. The cumulative output is analyzed for trends in failure probability and the design is altered to enhance its reliability, repeating the process until the desired level of reliability is achieved. The resulting design is optimal for the imposed conditions, and compared to a structure designed with a traditional factor of safety approach, is either lighter or more reliable. This demonstration revealed that for similar reliabilities, a stochastically designed wing was 20% lighter than a wing strengthened by the factor of safety. The major drawback in applying the method of stochastic finite element analysis is that very large, complex models can require extraordinary amounts of computer resources. Keywords: These, ASTROS computer program, ASTROS(automated structural optimization system).

The paper is the second in the series addressing the h-p version of the finite element method for parabolic equations. The present paper addresses the case when in both variables, the spatial and time, the h-p version is used. Error estimation is given and numerical computations are presented. In both cases we used the same p and q in all time intervals. The results show that the flexibility of the method, when properly employed, leads to the large increase of computational effectivity. Various adaptive approaches here will very effective tools for such an optimal choice. These aspects will be addressed in the forthcoming paper. (jhd)

A hypothesis is made that the Galerkin Finite Element Method (GFEM) offers a viable option to the traditional Finite Difference Method (FDM) for numerical weather prediction. The shallow water barotropic primitive equations are the forecast equations for all experiments. The hypothesis is tested by observing simple, analytic atmospheric wave propagation on uniform and variable mesh grids. Second, a strongly forced solution simulating small scale nonlinear interactions is evaluated for both the GFEM and FDM. Finally, a variable, moving grid for a GFEM model is compared to a uniform, higher resolution GFEM model for a strong vortex in a mean flow. The GFEM shows a better propagation for simple atmospheric waves and better prediction to a forced nonlinear solution than the FDM model. A moving variable grid follows an area of strong gradients while not generating noise in the transition zone. (Author)

A method of analyzing laminated-composite, linear-elastic plate and shell structures has been developed based on the hybrid stress finite-element model. Flat-plate elements are used for both plate and shell structures. Three quadrilateral elements designated by ELEM1, ELEMZ, and ELEMR, all with linear in-plane boundary displacement and linear in-plane stress assumptions, are chosen for use. Transverse shear deformation effects, and rotary as well as in- plane inertia, are included in all of these elements. The ELEM1 element can be applied to single-layer thin or moderately thick plates and shells. The ELEMR element can be applied to multilayer thin plates and shells, and the ELEMZ element may be used to analyze single-layer or multilayer, thin or thick plates and shells.

A new quadrilaterial finite element for the problem of bending of a uniform, homogeneous, isotropic, flat plate having an arbitrary number of nodal points and allowing an arbitrary level of refinement is developed from solution functions to the governing differential equation. Interelement continuity to the appropriate level of normal derivatives is provided in least error fashion by the use of spline functions for the edge displacement quantities and minimization by the Galerkin technique. Even for general quadrilateral domains no numerical quadrature is required for developing this finite element since all required integrals are taken over straight boundary edges and can be evaluated explicitly. With this new type of element, an improvement in accuracy is expected to result when large quadrilateral regions are modeled by a single element with an appropriate number of edge nodal points, because the error of this finite element approximation is associated with the boundary region of the elements. The force vector corresponding to the transverse pressure is derived from a series solution to the inhomogeneous differential equation, so that the effect of the forcing function in the element interior can be evaluated to any degree of accuracy desired. (Author)

This thesis is a continuation of a previous effort which developed a finite element solution of Schrodinger's Equation. The purpose of this research is to extend this previous work, and develop a chemical laser engineering tool for the identification of transition lines. Identification of laser transitions for a new chemical gain medium requires knowledge of Einstein's Coefficients. These transitions rates can be obtained by solving Schrodinger's Equation for diatomic molecules using the method of finite elements. Experimental vibrational eigenvalues for a given electronic state are used to determine the molecular potential surface which yields the closest numerical result. A non-linear minimization routine is used to hunt for this surface by adjusting parameters of energy functions such as the Harmonic, Morse, Lennard-Jones, and Mie potentials. For each set of new parameters selected by the minimization routine, the method of finite elements is used to solve Schrodinger's Equation. The eigenvalues from these solutions are then compared to the experimental values. Through this iterative process, the best potential surface is isolated. Franck Condon factors, which are proportional to Einstein's coefficients, can be computed with the numerical eigenfunctions from two different potential surfaces found in this way.

Babuska and Oh have introduced a new approach called the Method of Auxiliary Mapping(MAM), to deal with elliptic boundary value problems with singularities. In this paper this method is extended so that it can handle the plane elasticity problems containing singularities. In order to show the effectiveness, this method is compared with the conventional approach in the framework of the p-version of the finite element method. Moreover, it is demonstrated that this method yields a reasonable solution for those elasticity problems containing strong singularities which even can not be solved by using the h-p version of the finite element method.

The numerical solution of singular boundary value problems have been studied by several authors. The finite difference methods and its theory for a type of two-dimensional singular boundary value problems are given in (10), (13). The finite element method for axisymmetric elastic solid is proposed in (16). (5), (11), (14) and (20), gives a proof of the convergence of the finite element methods for one dimensional singular problems. (12) proves the 'optimal' order of convergence for the method of (16) provided the loads are axisymmetric and the solution is in C to the k + one power (bar omega). The convergence of the linear finite element method for two dimensional singular Dirichlet problem is proved in (18). (Author)

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In this paper, finite element heat transfer analysis of a 3D  orthogonal woven C-SiC composite is presented. Thermal  transport properties of the composite are predicted in the  three orthogonal directions. The effect of different  manufacturing porosity types on thermal transport  characteristics of the composite is also determined, which is  achieved by using four unit cells constructed at different  length scales. The predictive capability of the finite element  models is benchmarked against the experimental results  obtained from laser flash technique.

In this paper, finite element heat transfer analysis of a 3D  orthogonal woven C-SiC composite is presented. Thermal  transport properties of the composite are predicted in the  three orthogonal directions. The effect of different  manufacturing porosity types on thermal transport  characteristics of the composite is also determined, which is  achieved by using four unit cells constructed at different  length scales. The predictive capability of the finite element  models is benchmarked against the experimental results  obtained from laser flash technique.

In this paper, finite element heat transfer analysis of a 3D  orthogonal woven C-SiC composite is presented. Thermal  transport properties of the composite are predicted in the  three orthogonal directions. The effect of different  manufacturing porosity types on thermal transport  characteristics of the composite is also determined, which is  achieved by using four unit cells constructed at different  length scales. The predictive capability of the finite element  models is benchmarked against the experimental results  obtained from laser flash technique.

In this paper, finite element heat transfer analysis of a 3D  orthogonal woven C-SiC composite is presented. Thermal  transport properties of the composite are predicted in the  three orthogonal directions. The effect of different  manufacturing porosity types on thermal transport  characteristics of the composite is also determined, which is  achieved by using four unit cells constructed at different  length scales. The predictive capability of the finite element  models is benchmarked against the experimental results  obtained from laser flash technique.

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

A study was undertaken to investigate the measurement of wing deformation and internal loads using measured strain data. Future aerospace vehicle research depends on the ability to accurately measure the deformation and internal loads during ground testing and in flight. The approach uses the inverse Finite Element Method (iFEM). The iFEM is a robust, computationally efficient method that is well suited for real-time measurement of real-time structural deformation and loads. The method has been validated in previous work, but has yet to be applied to a large-scale test article. This work is in preparation for an upcoming loads test of a half-span test wing in the Flight Loads Laboratory at the National Aeronautics and Space Administration Armstrong Flight Research Center (Edwards, California). The method has been implemented into an efficient MATLAB® (The MathWorks, Inc., Natick, Massachusetts) code for testing different sensor configurations. This report discusses formulation and implementation along with the preliminary results from a representative aerospace structure. The end goal is to investigate the modeling and sensor placement approach so that the best practices can be applied to future aerospace projects.

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

A finite element program based on the plane stress assumption is developed and applied to elasto-plastic fracture problems involving monotonically increasing loads. The program directly predicts the initiation and propagation of fracture in the structure. That is, the concept of stress intensity factor is not utilized in the present approach. The approach uses a piecewise linear approximation of the actual stress-strain curve for the material, and the maximum strain criteria to predict both the yield and fracture. An incremental loading technique is employed to load the structure, and a zero modulus-unload reload scheme is developed to handle the response of the structure at fracture. Comparisons with published data on a cracked panel, and the experimental data obtained during this study on tensile and cracked specimens show that this finite element program can accurately predict load and deflection at fracture, load-deflection curves, fracture initiation locations, and stable or unstable crack propagation. This approach is shown to be highly dependent on the mesh density in areas of high strain gradients.

The theory of the computable a-posteriori error estimate for a finite element method is developed. Among other things, it is shown that the error estimate is very reliable and the ratio (called effectivity index) between the estimator and the true error approaches one. Numerical examples computed by program FEARS (Finite Element Adaptive Research Solver) of the University of Maryland, illustrate the effectivity and reliability of the estimators. (Author)

A summary and bibliography are presented of the investigations of structural inelasticity. Research conducted under this contract included two distinct projects. The first was concerned with using simple truss models to illustrate certain critical aspects of nonlinear material behavior. The other project was concerned with using a constant-strain finite element method to find complete solutions for the stress and displacement in a plate with a centered crack. The elastic solution was obtained first. The elastic/plastic solution was completed after the expiration of this contract. Keywords: Plasticity; Finite element analysis.

The problems of external flows around aircraft, internal flows inside propulsions units and also related problems like structural designs all require more and more accurate solutions while incorporating state of the art features involving more and more complex geometries and loadings. This is steadily becoming beyond the reach of analytical solution methods and thus necessitates the use of new computational methods. One of these is the Finite Element Method. The Finite Element Method was initially developed and used by Zienkiewicz for elasticity problems and is at the height of its development at the time of writing. The method is being studied theoretically as well as being applied to a broader and broader range of problems; its applications are found in solid mechanics, fluid mechanics, electromagnetics, etc. Some FORTRAN programs have been written in order to apply the Finite Element Method to the solution for low Reynolds number, incompressible flows around a Joukowski aerofoil, with emphasis on the generation of grids. These programs serve as evaluation tools and as a first step in a planned longer-term study of the Finite Element Method as applied to fluid flow problems.

In order to adequately understand the vibratory characteristics of electromechanical sonar transducers, two sophisticated techniques, the finite element method and state-of-the-art computer graphics, have been successfully combined. This process has for the first time vividly demonstrated the normal mode behavior of a Navy sonar transducer. This paper briefly describes the actual transducer being analyzed as well as the method used, gives results for the first three constant voltage drive resonant frequencies, and shows how computer graphics plays a key role in any such endeavor.

It has been theoretically shown that exponential rate of convergence in the energy norm can be obtained by a proper combination of the h- and p- extension of the finite element method for essentially all engineering problems in plane elasticity, including those with singularities in the exact solution. In this paper we present an expert system frame, which guides the user to an optimal selection of the mesh and degree distribution. After a crude preliminary computation the expert system predicts the performance of various mesh and degree combinations and provides the analyst with rational support for his decisions about the mesh design. Numerical examples show that the suggested approach gives superior results with the minimum effort in human data preparation and computer time. Keywords: Adaptive methods; and Error estimations.

The paper addresses the performance of square elements of type Q(p) and Q'(p) . (The Q(p) resp. Q'(p) are elements of degree p analogous to the well known 9 and 8 noded elements for p = 2.) The performance is analyzed theoretically for the class of analytic functions. Numerical experiments confirm the conclusions drawn from the theory. The computational complexity of a solution algorithm is studied using timings of the computation on an Alliant FX/8 computer. The data show that high order elements are preferable.

In this paper, the fundamental theoretical ideas behind the relatively recent p- version and h-p version are discussed. In the p-version, a fixed mesh is used and p is allowed to increase. The h-p version combines both approaches. The basic properties and characteristics of these newer versions, especially in areas where their behavior is significantly different from that of the h-version, are described and explained.

The purpose of this report is to develop a model of non-uniform beams within a software environment that lends itself to design, simulation, and analysis of dynamic systems. The beam is modeled by the Euler-Bernoulli approximation using the finite element method. Reformulation of the second-order symmetric beam equations into the fIrst-order state-space domain enables dynamic analysis and design from within the modern control paradigm. The MATLAB software package is chosen as it is the current state-of-the-art modeling environment for control engineering. This report will present the development of the modeling software, develop some of the underlying theory and limitations of the analysis, demonstrate its use in the dynamic modeling and analysis of an XM291 gun system, and validate its results against known analytic results.

The Eulerian equations are solved by use of the finite element method (FEM) in conjunction with the Galerkin method of weighted residuals. The unsteady, nonconservative form of the equations is used to obtain the steady- state solution. Modifications are made in the time integration to improve stability at the cost of sacrificing the transient behavior. Numerical results are presented which compare reasonably well with other numerical solutions and with experimental data for transonic flow over airfoils.

A finite-element structural model has been developed for the dynamic analysis of laminated, thick plates. The model uses constant thickness quadrilateral elements to represent the shape of the plate and these elements are stacked in the thickness direction to represent the desired material layers. The analysis allows for orthotropic material properties of each layer as well as for elastic-plastic material response. Nonlinear strain displacement relations are used in the formulation to represent large, transverse plate deflections. The finite-element model is used to prepare a computer program for the numerical calculations. Two versions of the program have been prepared, which correspond to two different time integration numerical methods. These methods include finite-difference and predictor-corrector techniques. The computer programs are designed for time and space dependent pressure loads to be applied to one surface of the plate. However, the programs could be used for other loading conditions by changing one subroutine.