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The structures of odd-odd $N=Z$ nuclei in the lower \emph{fp} shell have been investigated with a new isospin-nonconserving microscopical interaction. The interaction is derived from a high-precision charge-dependent Bonn nucleon-nucleon potential using the folded-diagram renormalization method. Excellent agreements with experimental data have been obtained up to band terminations. Particularly, the relative positions of T=0 and T=1 bands were well reproduced. Calculations with another interaction obtained from the Idaho-A chiral potential showed similar results. Our calculations also give a good description of the existence of high-spin isomeric states in the $0f_{7/2}$ sub-shell. As examples, the spectroscopies and isospin structures of $^{46}$V and $^{50}$Mn have been discussed in detail, with the useful predictions of level structures including electromagnetic properties. Results for $^{50}$Mn were analyzed where experimental observations are still insufficient.

The analysis and design of robust controllers for multivariable discrete-time feedback systems in the frequency domain are studied. The robustness stability conditions for discrete-time systems with additive alteration, and with multiplicative alteration are developed. The robust LQG/LTR method has been extended from the continuous-time system to the discrete-time system. It has been proven that the LQG/LTR method is also valid for the LQG control of the discrete-time system with the filtering observer. As an application of the LQG/LTR technique for discrete-time systems, the design of reduced order optimal digital LQG controllers for the orbiting flexible shallow spherical shell system is considered. The comparison between the digital optimal LQG controller with the filtering observer and with the predicting observer for the orbiting flexible shallow spherical shell has been made.... Digital control, Large space structures, LQG/LTR method for discrete-time system, Robust controller design, Design of reduced order LQG controller.

The problem of optimum design of axially compressed cylinders\nstiffened by rings and stringers is discussed. Particular attention is devoted to configurations suitable for large launch vehicles. Consideration is given to the analytical techniques for determining strength as well as the procedure for optimization.

Early experimental results on the buckling of circular cylindrical shells subject to axial impact are described. A hypothesis for the mechanism of buckling which was based on these experiments is described. The results of further experiments which were designed to test predictions from the hypothesis and which appear to verify it in several aspects are then described.

In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to know and speak the laws that govern them. (For more information: 12 Tables of Code ) Name of Legally Binding Document: BS NA EN 1999-1-5: UK National Annex to Eurocode 9. Design of aluminium structures. Shell structures Name of Standards Organization: British Standards Institution (BSI) LEGALLY BINDING DOCUMENT

Mathematics of nonlinear dynamics of thin walled shell structures

To determine the elastic buckling pressure of simply supported cylindrical shells subjected to lateral end axial hydrostatic forces, various versions of linear bending theories have been employed in the past. For certain shell dimensions, however the expressions commonly\nused may yield substantially differing results. In what follows, recent work on this problem by A. E. Armenakas and the writer is briefly reviewed. This work consisted primarily in employing a general\nbending theory of circular cylindrical shells under the influence of initial stress, developed earlier by the same authors, to re-examine the problem mentioned, and compare the results with those of previous investigations. The outcome was the establishment of a simple but accurate expression for the buckling pressure applicable to a wide range of shell dimensions.

To determine the elastic buckling pressure of simply supported cylindrical shells subjected to lateral end axial hydrostatic forces, various versions of linear bending theories have been employed in the past. For certain shell dimensions, however the expressions commonly\nused may yield substantially differing results. In what follows, recent work on this problem by A. E. Armenakas and the writer is briefly reviewed. This work consisted primarily in employing a general\nbending theory of circular cylindrical shells under the influence of initial stress, developed earlier by the same authors, to re-examine the problem mentioned, and compare the results with those of previous investigations. The outcome was the establishment of a simple but accurate expression for the buckling pressure applicable to a wide range of shell dimensions.

A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.

Semiclassical periodic-orbit theory (POT) is applied to the physics of nuclear structures, with the use of a realistic nuclear mean-field model given by the radial power-law potential. Evolution of deformed shell structures, which are responsible for various nuclear deformations, are clearly understood from the contribution of short classical periodic orbits (POs). Bifurcations of short POs, which imply underlying local dynamical symmetry, play significant role there. The effect of the spin degree of freedom is also investigated in relevance to the pseudospin symmetry in spherical nuclei and the prolate-oblate asymmetry in shell structures of nuclei with quadrupole-type deformations.

Described are the mathematical model and solution methodologies for analyzing the structural response of thin, metallic elasto-viscoplastic shell structures under large thermomechanical loads and their non-isothermal buckling behavior. Among the system responses associated with these loads and conditions are snap-through, buckling, thermal buckling, and creep buckling. This geometric and material nonlinearities (of high order) can be anticipated and are considered in the model and the numerical treatment.

This article is devoted to the simultaneous optimization of shape and topology of shell structures. The optimum shape is obtained together with the optimum layout for the reinforcement layers at the both sides of the shell surface. To solve this problem the finite element method is employed. It is assumed that each element is comprised of a porous media with microscopic rectangular voids where the density of the material in each element is a function of the geometric parameters of the voids. These parameters are also considered as the design variables of the topology optimization problem. The geometry of the shell structure is defined by using Non-Uniform Rational B-Splines (NURBS) technique and the control points of the NURBS’ surfaces are considered as the design variables of the shape optimization problem. For solution the Method of Moving Asymptotes (MMA) is employed. To demonstrate the efficiency of the method a few examples are presented and the results are discussed.

The particle density distribution emerging from the solution of the Vlasov equation for relativistic, non-interacting particles with spherically symmetric initial conditions is shown to exhibit a shell-like structure for late fixed times in the center-of-mass (CM) frame of the system. A similar phenomenon was recently observed employing the test-particle method to solve the Vlasov equation for quarks with Nambu-Jona-Lasinio-type interactions, and was attributed to the attractive forces among the particles. Contrary to this claim, it is demonstrated here that this effect is of purely relativistic origin and is sensitive only to the mass of the particles and their initial phase-space distribution.

In this work nuclear structure properties of $^{86,87,88,89}$Y isotopes have been investigated using large-scale shell-model calculations within the full $f_{5/2}pg_{9/2}$ model space. The calculations have been performed with JUN45 and jj44b effective interactions that have been proposed for use in the $f_{5/2}$, $p_{3/2}$, $p_{1/2}$, $g_{9/2}$ model space for both protons and neutrons. Reasonable agreement between experimental and calculated values are obtained. This work will add more information to previous study by projected shell model [Eur. Phys. J. A 48, 138 (2012)] where full-fledged shell model calculations proposed for these nuclei.

In this work nuclear structure properties of $^{86,87,88,89}$Y isotopes have been investigated using large-scale shell-model calculations within the full $f_{5/2}pg_{9/2}$ model space. The calculations have been performed with JUN45 and jj44b effective interactions that have been proposed for use in the $f_{5/2}$, $p_{3/2}$, $p_{1/2}$, $g_{9/2}$ model space for both protons and neutrons. Reasonable agreement between experimental and calculated values are obtained. This work will add more information to previous study by projected shell model [Eur. Phys. J. A 48, 138 (2012)] where full-fledged shell model calculations proposed for these nuclei.

A mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is disussed. Among the system responses, which are associated with these load conditions, are thermal buckling and creep buckling. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and have been considered in the development of the mathematical model. Furthermore, this was accommodated in the solution procedures. A complete true ab-inito rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformation, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of the metric and curvature in two coordinate systems, a fixed (spatial) one and a convected (material) coordinate system. The relations between the time derivative and the covariant derivatives (gradients) have been developed for curved space and motion, so that the velocity components supply the connection between the equations of motion and the time rate of change of the metric and curvature tensors.

Shell analysis manual provides methods for determining static deflections and internal load and stress distributions in shells under various loading conditions, and methods of analyzing static instability of shell structures. Also included are methods for determining the lightest shell wall for various constructions.

Shell analysis manual provides methods for determining static deflections and internal load and stress distributions in shells under various loading conditions, and methods of analyzing static instability of shell structures. Also included are methods for determining the lightest shell wall for various constructions.

Recent theoretical and experimental research is briefly described to trace the development of deformation and the occurrence of collapse in pressurized circular cylindrical membranes under applied moment loading. The collapse of pure membrane cylinders is then compared with instability of pressurized cylindrical shells. This approach leads to a better understanding of the behavior of pressurized cylinders under bending loads. The results suggest possibilities for further research utilizing the membrane approach.

Investigations carried out at STL on three current problems involving instability of thin shells in applications to aerospace vehicles are discussed. The first concerns the experimental determination of the buckling behavior of longitudinally stiffened pressurized cylinders; the\nsecond, the analytic prediction and experimental confirmation of the buckling behavior of multi-layer cylinders and the third involves the behavior of cylinders under combined axial load and lateral pressure. In each case the background of the application is reviewed, followed by a short description of the work. It is indicated that the longitudinally stiffened cylinder shows considerable promise in taking maximum advantage of the strengthening effect of internal pressure, that the use of an external low modulus layer as an insulator can have a significant effect on the buckling capability of a shell, and that the assumption of a linear interaction for\npressure and axial load is unnecessarily conservative.

General instability in shell type structures is a relatively infrequent phenomenon. By general instability is meant that a complete section of a structure becomes elastically unstable, as compared with local crippling or buckling. The first step in design is to rough size the structure and determine its compatibility with air vehicle configuration and system instillations. After this step has been completed, it is possible to survey the layouts to determine whether general instability is likely to occur. The general parameters of length, diameter, frame spacing, element stiffness, etc., are than investigated to determine if a general failing stress exists which is less than any local column, beam column, or panel failing stress. In this way, a well-balanced design is determined and general stability failing modes eliminated.

Some theoretical investigations of buckling of elastic shells are surveyed in this report. Only geometrically perfect shells are considered; initial dents and out-of-roundness are not taken into account. Several questions raised by the studies are: (a) Under what conditions is the infinitesimal theory of buckling of shells adequate? (b) How does the energy theory of buckling of shells correlate with the method based on equilibrium equations for bending moments, tensions, and shears in a buckled configuration? (c) How important are nonlinear terms in the tangential displacements u, v in the strain-displacement relations for buckling and post-buckling studies? (d) How important are the boundary conditions for u, v in affecting stability? (e) If a condition of snap-through is approached, how much external work is required to push the shell \"over the hump\" into the buckled configuration? (f) How reliable are mathematical approximations used previously in the infinitesimal theory of buckling of shells? Tentative and incomplete answers to some of these questions are suggested.

Techniques have been developed for making essentially \"perfect\" thin cylindrical shells and for making shells with definite types of initial deformations. The \"perfect\" shells give buckling stresses much higher than have previously been obtained. Initial deformations of the form ∆R= a(o) sin ((πx)/L) have been tested and ranges of positive a(o) were found in which there was no lowering of the buckling stress. Negative values of a(o) caused a decrease in the failure load. A theoretical solution which indicated the same trends as were found experimentally has been carried out.

Several theoretical and experimental investigations on the buckling of cylinders due to both axial and circumferential thermal stresses are reviewed. Differences that exist among the various results are discussed and areas of future work are indicated.

Theoretical buckling coefficients are obtained for the general instability of simply supported, corrugated core sandwich circular cylinders under combined loads with the core oriented parallel to the longitudinal axis of the cylinder. Buckling curves are presented for axial\ncompression, external lateral pressure, torsion, and some typical interactions. The differential equations of equilibrium used to obtain the buckling equations were derived from the small deflection equations of Stein and Mayer which include the effect of deformation due to transverse shear. These equations are solved by Galerkin's equation. Remarks are made concerning the probable validity of the results of the small deflection theory for sandwich shells.

In order to promote public education and public safety, equal justice for all, a better informed citizenry, the rule of law, world trade and world peace, this legal document is hereby made available on a noncommercial basis, as it is the right of all humans to know and speak the laws that govern them. (For more information: 12 Tables of Code ) Name of Standards Organization: Bureau of Indian Standards (BIS) Committee Designation: CED 38 Designator of Legally Binding Document: IS 2210 : 2023 Title of Legally Binding Document: Criteria For Design Of Reinforced Concrete Shell Structures And Folded Plates Number of Amendments: 0 Status: Active Additional Info: LEGALLY BINDING DOCUMENT Step Out From the Old to the New --Jawaharlal Nehru

We investigate the folding transition of a single diblock copolymer consisting of a semiflexible and a flexible block. We obtain a {\it Saturn-shaped} core-shell conformation in the folded state, in which the flexible block forms a core and the semiflexible block wraps around it. We demonstrate two distinctive features of the core-shell structures: (i) The kinetics of the folding transition in the copolymer are significantly more efficient than those of a semiflexible homopolymer. (ii) The core-shell structure does not depend on the transition pathway.

Large deflection theory is used to compute buckling loads of simply supported initially perfect cylinders under axial compression, external hydrostatic pressure, and combinations of axial compression and internal or external pressure. Important results are obtained by taking into account prebuckling deformations and stresses induced by edge support. For example, the presence of these deformations and stresses can decrease the axial-compression buckling load of an unpressurized perfect cylinder by 50 percent or more.

Experimental and theoretical studies have been carried out to investigate the stability of ring-stiffened cylinders and hemispherical shells under hydrostatic pressure. The use of accurately machined models has been found extremely valuable in improving the quality of experimental data, thereby permitting a more careful examination of theory. As a result, the effects of boundary conditions and other factors usually masked by the influence of structural imperfections have been clarified.\n\nSo far these studies have caused the investigators to regard classical small-deflection theory with increasing confidence.

Final report for period Jan 1987 - Jun 1997

The finite element method has proven to be an invaluable tool for analysis and design of complex, high performance systems, such as bladed-disk assemblies in aircraft turbofan engines. However, as the problem size increase, the computation time required by conventional computers can be prohibitively high. Parallel processing computers provide the means to overcome these computation time limits. This report summarizes the results of a research activity aimed at providing a finite element capability for analyzing turbomachinery bladed-disk assemblies in a vector/parallel processing environment. A special purpose code, named with the acronym SAPNEW, has been developed to perform static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements. SAPNEW provides a stand alone capability for static and eigen analysis on the Alliant FX/80, a parallel processing computer. A preprocessor, named with the acronym NTOS, has been developed to accept NASTRAN input decks and convert them to the SAPNEW format to make SAPNEW more readily used by researchers at NASA Lewis Research Center.

The deformation and complete stress distribution are determined for each of the following edge loaded thin shells of revolution: (1) a right circular cylinder, (2) a frustum of a right circular cone, and (3) a portion of a sphere. The locations of the maximum circumferential and meridional stresses on both the inner and outer surfaces are also found. The basic equations for the above were selected from the published literature on the subject and expanded to produce to resultant-stress equations in closed from where practicable to do so. Equations are also developed for the discontinuity shear force and bending moment at each of the following junction: (1) axial change of thickness in a circular cylinder, (2) axial change of thickness in a cone, (3) change of thickness in a portion of a sphere, (4) a cylinder and a cone, (5) a cylinder and a portion of a sphere(6) a cylinder and a flat head, and (7) a cone and a portion of a sphere.

Parametric studies were performed to assess the effects of various parameters on the free-vibration behavior (natural frequencies) of (+/- theta)(sub 2) angle-ply, fiber composite, thin shell structures in a hygrothermal environment. Knowledge of the natural frequencies of structures is important in considering their response to various kinds of excitation, especially when structures and force systems are complex and when excitations are not periodic. The three dimensional, finite element structural analysis computer code CSTEM was used in the Cray YMP computer environment. The fiber composite shell was assumed to be cylindrical and made from T300 graphite fibers embedded in an intermediate-modulus, high-strength matrix. The following parameters were investigated: the length and the laminate thickness of the shell, the fiber orientation, the fiber volume fraction, the temperature profile through the thickness of the laminate, and laminates with different ply thicknesses. The results indicate that the fiber orientation and the length of the laminated shell had significant effects on the natural frequencies. The fiber volume fraction, the laminate thickness, and the temperature profile through the shell thickness had weak effects on the natural frequencies. Finally, the laminates with different ply thicknesses had an insignificant influence on the behavior of the vibrated laminated shell. Also, a single through-the-thickness, eight-node, three dimensional composite finite element analysis appears to be sufficient for investigating the free-vibration behavior of thin, composite, angle-ply shell structures.

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three optimisation examples, namely a catenary, roof over a rectangular domain and freeform architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.

The differential equations which must be solved to predict the buckling load are reviewed. The different possible physical interpretations of these equations are discussed.

The problem of buckling of clamped shallow spherical shells has recently been considered in several theoretical investigations. Buck-ling loads under uniform external pressure were obtained in these investigations which show a surprisingly good agreement with each other, but show a marked disagreement with available experimental values. In all previous studies it has been assumed that the shell deformations are rotationally symmetric. In this paper, the buckling problem is re-examined by introducing asymmetric modes of deformation. The approach is to superimpose small asymmetric deflections on finite axisymmetric deflections, and to show that the symmetric states of deformation are unstable over certain ranges of load and geometry parameter. Numerical results are obtained by means of a digital computer and are compared with previous theoretical and experimental results.

The problem of buckling of clamped shallow spherical shells has recently been considered in several theoretical investigations. Buck-ling loads under uniform external pressure were obtained in these investigations which show a surprisingly good agreement with each other, but show a marked disagreement with available experimental values. In all previous studies it has been assumed that the shell deformations are rotationally symmetric. In this paper, the buckling problem is re-examined by introducing asymmetric modes of deformation. The approach is to superimpose small asymmetric deflections on finite axisymmetric deflections, and to show that the symmetric states of deformation are unstable over certain ranges of load and geometry parameter. Numerical results are obtained by means of a digital computer and are compared with previous theoretical and experimental results.

The problem of buckling of clamped shallow spherical shells has recently been considered in several theoretical investigations. Buck-ling loads under uniform external pressure were obtained in these investigations which show a surprisingly good agreement with each other, but show a marked disagreement with available experimental values. In all previous studies it has been assumed that the shell deformations are rotationally symmetric. In this paper, the buckling problem is re-examined by introducing asymmetric modes of deformation. The approach is to superimpose small asymmetric deflections on finite axisymmetric deflections, and to show that the symmetric states of deformation are unstable over certain ranges of load and geometry parameter. Numerical results are obtained by means of a digital computer and are compared with previous theoretical and experimental results.

The development of a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads is examined. In the mathematical model, geometric as well as material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

A numerical method is presented for the stress analysis of stiffened-shell structures of arbitrary cross section under nonuniform temperature distributions. The method is based on a previously published procedure that is extended to include temperature effects and multicell construction. The application of the method to practical problems is discussed and an illustrative analysis is presented of a two-cell box beam under the combined action of vertical loads and a nonuniform temperature distribution.

Results of tests on postbuckling equilibrium positions of isotropic thin-walled circular cylindrical shells under axial compression, external pressure and combined loading are reported and compared with available theoretical results.

This article is from Nanoscale Research Letters , volume 7 . Abstract Aluminum nanocontact conductance histograms are studied experimentally from room temperature up to near the bulk melting point. The dominant stable configurations for this metal show a very early crossover from shell structures at low wire diameters to ionic subshell structures at larger diameters. At these larger radii, the favorable structures are temperature-independent and consistent with those expected for ionic subshell (faceted) formations in face-centered cubic geometries. When approaching the bulk melting temperature, these local stability structures become less pronounced as shown by the vanishing conductance histogram peak structure.

This article is from Nanoscale Research Letters , volume 7 . Abstract Aluminum nanocontact conductance histograms are studied experimentally from room temperature up to near the bulk melting point. The dominant stable configurations for this metal show a very early crossover from shell structures at low wire diameters to ionic subshell structures at larger diameters. At these larger radii, the favorable structures are temperature-independent and consistent with those expected for ionic subshell (faceted) formations in face-centered cubic geometries. When approaching the bulk melting temperature, these local stability structures become less pronounced as shown by the vanishing conductance histogram peak structure.

The primary theme is the nonlinear behavior of shell structures. A general formulation that can be applied to all structures is derived and then specialized for application to shells through the development of a quadrilateral shell finite element. The formulation is in incremental form and is derived in terms of the material coordinate system. The quadrilateral shell element which is introduced uses the exact geometry of the shell surface in the computation of stiffness matrices and loads. A consistent method is used for transforming the element and its properties; this improves element effectiveness for application to branched and reinforced shells. The shell surface geometry is used in the enforcement of the continuity of displacements for satisfying the convergence requirements. The ability of the element to undergo rigid body motion without causing strains is examined by studying the eigenvalues of the stiffness matrix of an element.

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

A general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads is considered. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and ratchetting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model.

A computer program for analyzing axisymmetric shells with inertial forces caused by rotation about the shell axis is developed by revising the STARS II shell program. The basic capabilities of the STARS II shell program, such as the treatment of the branched shells, stiffened wall construction, and thermal gradients, are retained.

A discussion of the current methods used to design the Saturn type booster shell structures is presented covering bending and axial compression, with and without internal pressure. Problem areas encountered in the application of available shell stability data to these designs are delineated; as well as, suggested areas of future research for shell configurations anticipated in advanced designs.

The authors give a brief account of some of their recent analytical and numerical studies of cone buckling. limiting the discussion to axisymmetric deformations.\n\nPertinent numerical results for the relaxation buckling of full cones subjected to uniform external pressure and Belleville springs deformed by axial edge loads are presented. In addition. bifurcation buckling problems are discussed. For a specific case. the existence of Friedrichs' intermediate buckling load, P(m). as applied to cones. is established. Upper and lower bounds for its value are given.

A study of anomalous scaling in models of passive scalar advection in terms of singular coherent structures is proposed. The stochastic dynamical system considered is a shell model reformulation of Kraichnan model. We extend the method introduced in \cite{DDG99} to the calculation of self-similar instantons and we show how such objects, being the most singular events, are appropriate to capture asymptotic scaling properties of the scalar field. Preliminary results concerning the statistical weight of fluctuations around these optimal configurations are also presented.