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Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

This final report summarizes work on a three-year project devoted to dynamic friction and on control of systems with frictional forces. Detailed theoretical and numerical studies of static and dynamic friction and various phenomena of dynamic friction (stick-slip motion, self-excited oscillations, frictional damping, etc.) are described. Included in the report is also a study of methods of statistical homogenization, devised to develop new micromechanics-based models of contact and friction. The question of optimal control with distributed dynamical systems of viscoelastic bodies with frictional forces is also described. A final component of this study focuses on the mathematical and numerical analysis of elastohydrodynamic lubrication problems and is included in the final chapter. The studies presented in this report provide both a theoretical and numerical basis for modeling contact and friction. These models are shown to produce results in very good qualitative and quantitative agreement with experimental results. Keywords: Friction, Damping, Structural dynamics, Elastohydrodynamic lubrication.

(500)p. ; 23 cm

(500)p. ; 23 cm

We present the algebraic foundations of the symmetric Zassenhaus algorithm and some of its variants. These algorithms have proven effective in devising higher-order methods for solving the time-dependent Schr\"{o}dinger equation in the semiclassical regime. We find that the favourable properties of these methods derive directly from the structural properties of a Z2-graded Lie algebra. Commutators in this Lie algebra can be simplified explicitly, leading to commutator-free methods. Their other structural properties are crucial in proving unitarity, stability, convergence, error bounds and quadratic costs of Zassenhaus based methods. These algebraic structures have also found applications in Magnus expansion based methods for time-varying potentials where they allow significantly milder constraints for convergence and lead to highly effective schemes. The algebraic foundations laid out in this work pave the way for extending higher-order Zassenhaus and Magnus schemes to other equations of quantum mechanics.

This document is the final technical report for the project, Computational Methods in Nonlinear Mechanics. The Report summarizes results obtained on this project for the period June 30, 1980 through September 30, 1982. All objectives of the original statement of work have been accomplished. These have included advances in mathematical modelling, numerical analysis, approximation theory, development of computer codes, and the study of related issues connected with the following nonlinear structural problems: contact problems in elasticity, reduced integration and penalty methods for finite element approximations of constrained problems in elasticity and fluid flow, contact problems with friction, nonlinear friction laws, plasticity and metal forming, existence and approximation theories in contact problem in elastostatics, fracture mechanics numerical methods for problems of finite elastic deformation, nonlinear eigenvalue problems, and bifurcation theory. Detailed summaries of results in some of these areas are given together with lists of all papers, reports, books, dissertations and oral presentations produced during the contract period. Suggestions for further research areas are also given. (Author)

This document is the final technical report for the project, Computational Methods in Nonlinear Mechanics. The Report summarizes results obtained on this project for the period June 30, 1980 through September 30, 1982. All objectives of the original statement of work have been accomplished. These have included advances in mathematical modelling, numerical analysis, approximation theory, development of computer codes, and the study of related issues connected with the following nonlinear structural problems: contact problems in elasticity, reduced integration and penalty methods for finite element approximations of constrained problems in elasticity and fluid flow, contact problems with friction, nonlinear friction laws, plasticity and metal forming, existence and approximation theories in contact problem in elastostatics, fracture mechanics numerical methods for problems of finite elastic deformation, nonlinear eigenvalue problems, and bifurcation theory. Detailed summaries of results in some of these areas are given together with lists of all papers, reports, books, dissertations and oral presentations produced during the contract period. Suggestions for further research areas are also given. (Author)

The primary objectives of this research are the development of algorithms which are applicable to non-linear continuum mechanic problems, especially to Stefan's Problems and Fluid Flows in Porous Media (Richard's Equation). We have studied 2-D and 3-D related problems. The codes are written in Cray Fortran and vectorization are done on the Cray Y-MP. The results obtained by Compact ADI, Finite Difference SOR and ADI are compared. It is seen that Compact ADI is superior. Six scientific research Papers have been presented/published in various conferences and journals in the last two years. All of the papers are attached in the appendix as attachments. Two senior faculty members worked in this project. Bolindra N. Borah (P.I.), Professor, North Carolina A&T State University, Robert E. White (Co-P.I.), Professor, North Carolina State University are the principal researchers. Besides, four graduate students participated in this project. Two have already completed the M.S. in Applied Mathematics while the other two are completing in the Spring Semester 1994.

The primary objectives of this research are the development of algorithms which are applicable to non-linear continuum mechanic problems, especially to Stefan's Problems and Fluid Flows in Porous Media (Richard's Equation). We have studied 2-D and 3-D related problems. The codes are written in Cray Fortran and vectorization are done on the Cray Y-MP. The results obtained by Compact ADI, Finite Difference SOR and ADI are compared. It is seen that Compact ADI is superior. Six scientific research Papers have been presented/published in various conferences and journals in the last two years. All of the papers are attached in the appendix as attachments. Two senior faculty members worked in this project. Bolindra N. Borah (P.I.), Professor, North Carolina A&T State University, Robert E. White (Co-P.I.), Professor, North Carolina State University are the principal researchers. Besides, four graduate students participated in this project. Two have already completed the M.S. in Applied Mathematics while the other two are completing in the Spring Semester 1994.

The primary objectives of this research are the development of algorithms which are applicable to non-linear continuum mechanic problems, especially to Stefan's Problems and Fluid Flows in Porous Media (Richard's Equation). We have studied 2-D and 3-D related problems. The codes are written in Cray Fortran and vectorization are done on the Cray Y-MP. The results obtained by Compact ADI, Finite Difference SOR and ADI are compared. It is seen that Compact ADI is superior. Six scientific research Papers have been presented/published in various conferences and journals in the last two years. All of the papers are attached in the appendix as attachments. Two senior faculty members worked in this project. Bolindra N. Borah (P.I.), Professor, North Carolina A&T State University, Robert E. White (Co-P.I.), Professor, North Carolina State University are the principal researchers. Besides, four graduate students participated in this project. Two have already completed the M.S. in Applied Mathematics while the other two are completing in the Spring Semester 1994.

In this report the dynamic behavior of metallic bodies subjected to dry frictional contacts is studied. A simple model of interface response which incorporates a constitutive equation for the normal deformability of the interface and the Coulomb law of friction is developed. This interface model is incorporated in the formulation of problems in continuum mechanics that invlove the contact of linearly elastic or viscoelastic bodies. Variational formulations for these problems are established and existence and uniqueness results are proved for steady-sliding and dynamic frictionless or frictional contact problems. The same interface model is also incorporated in finite dimensional models for contact problems: a simple rigid body model and finite element space discretizations of the continuum models. Numerical studies steady sliding and its dynamic stability are presented, as well as numerical studies of friction-induced oscillations. In the latter case, the Newmark method and the central-difference technique are used to integrate numerically the equations of motion. In the numerical studies particular emphasis is given to the role played by normal degree-of-freedom in frictional sliding.