Showing papers in "Computational Mechanics in 1995"
TL;DR: In this article, a procedure for coupling meshless methods such as the element-free Galerkin method with finite element methods is developed so that continuity and consistency are preserved on the interface elements.
Abstract: A procedure is developed for coupling meshless methods such as the element-free Galerkin method with finite element methods. The coupling is developed so that continuity and consistency are preserved on the interface elements. Results are presented for both elastostatic and elastodynamic problems, including a problem with crack growth.
452 citations
TL;DR: A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented and it is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids.
Abstract: A meshless approach to the analysis of arbitrary Kirchhoff plates by the Element-Free Galerkin (EFG) method is presented. The method is based on moving least squares approximant. The method is meshless, which means that the discretization is independent of the geometric subdivision into “finite elements”. The satisfaction of the C
1 continuity requirements are easily met by EFG since it requires only C
1 weights; therefore, it is not necessary to resort to Mindlin-Reissner theory or to devices such as discrete Kirchhoff theory. The requirements of consistency are met by the use of a quadratic polynomial basis. A subdivision similar to finite elements is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Lagrange multipliers. It is shown, that high accuracy can be achieved for arbitrary grid geometries, for clamped and simply-supported edge conditions, and for regular and irregular grids. Numerical studies are presented which show that the optimal support is about 3.9 node spacings, and that high-order quadrature is required.
278 citations
TL;DR: In this article, the concept of strong discontinuity analysis is introduced and driven, as a matter of example, into a standard continuum damage model, and the relevant features that make the constitutive equation compatible with the appearance of strongly discontinuities are extracted.
Abstract: Numerical simulation of strong discontinuities by using standard stress-strain constitutive equations including strain-softening is addressed. The concept of strong discontinuity analysis is introduced and driven, as a matter of example, into a standard continuum damage model. Then, the relevant features that make the constitutive equation compatible with the appearance of strong discontinuities are extracted. Those features are used in the design of a specific finite element approach to the strong discontinuity problem which is placed in the framework of the assumed enhanced strain methods. Numerical simulations show that mesh size and mesh alignment dependencies, typical of some continuum approaches, can be removed.
135 citations
TL;DR: In this article, the authors proposed a gridless Lagrangian technique called smoothed particle hydrodynamics (SPH) to analyze high deformation impulsive loading events.
Abstract: SPH (Smoothed Particle Hydrodynamics) is a gridless Lagrangian technique which is appealing as a possible alternative to numerical techniques currently used to analyze high deformation impulsive loading events. In the present study, the SPH algorithm has been subjected to detailed testing and analysis to determine the feasibility of using PRONTO/SPH for the analysis of various types of underwater explosion problems involving fluid-structure and shock-structure interactions. Of particular interest are effects of bubble formation and collapse and the permanent deformation of thin walled structures due to these loadings. These are exceptionally difficult problems to model. Past attempts with various types of codes have not been satisfactory. Coupling SPH into the finite element code PRONTO represents a new approach to the problem. Results show that the method is well-suited for transmission of loads from underwater explosions to nearby structures, but the calculation of late time effects due to acceleration of gravity and bubble buoyancy will require additional development, and possibly coupling with implicit or incompressible methods.
129 citations
TL;DR: In this paper, the authors reviewed gradient-enhanced damage and plasticity approaches with regard to their ability to model localization phenomena in quasi-brittle and frictional materials and highlighted the fundamental role of dispersion in setting the width of localization bands.
Abstract: Gradient-enhanced damage and plasticity approaches are reviewed with regard to their ability to model localization phenomena in quasi-brittle and frictional materials. Emphasis is put on the algorithmic aspects. For the purpose of carrying out large-scale finite element simulations efficient numerical treatments are outlined for gradient-enhanced damage and gradient-enhanced plasticity models. For the latter class of models a full dispersion analysis is presented at the end of the paper. In this analysis the fundamental role of dispersion in setting the width of localization bands is highlighted.
123 citations
TL;DR: The results of numerical tests demonstrate the feasibility of the proposed method, which includes a training phase and a recognition phase, to detect the existence and to identify the characteristics of damage in composite structures.
Abstract: This study examines the feasibility of using artificial neural network in conjunction with system identification techniques to detect the existence and to identify the characteristics of damage in composite structures. The methodology proposed here includes a training phase and a recognition phase. In the training phase, candidate models for structures with various types of damage are designated as the patterns. These patterns are organized into pattern classes according to the location and the severity of the damage. Then system identifications are performed to extract the transfer functions as the features of the structural systems. These transfer functions are fed into a multi-layer perceptron (MLP) as the input patterns for training. The MLP serves as a nearest neighborhood classifier. In the pattern recognition phase, a structure with unforeseen damage is classified within the closest class in the training set and the damage in the structure is identified as that of the class. The results of numerical tests demonstrate the feasibility of the proposed method.
108 citations
TL;DR: In this paper, the authors discuss strategies for restructuring the transport calculations so that the Eulerian formulation may be applied to a broader range of problems in science and engineering, and demonstrate the efficiency of the proposed strategies.
Abstract: An Eulerian formulation is necessary for the accurate solution of contact and impact problems involving penetration and fracture. The Eulerian mesh is fixed in space, thereby eliminating all the problems associated with a distorted mesh that are commonly encountered with a Lagrangian formulation. Since the material flows through the mesh, additional data is necessary in an Eulerian formulation to describe the current contents of an element and additional calculations must be performed to update the data. The additional calculations, which account for the material transport between the elements, are usually much more expensive than the Lagrangian terms in the calculation. As a consequence, Eulerian calculations have been restricted to hypervelocity impacts, which cannot be solved in any other manner. This paper discusses strategies for restructuring the transport calculations so that the Eulerian formulation may be applied to a broader range of problems in science and engineering. Example calculations, performed on a workstation, are presented to demonstrate the efficiency of the proposed strategies.
99 citations
TL;DR: In this article, the basic aspects of a damage mechanics approach for composites capable of simulating complete fracture phenomena are presented, and two material examples, ceramic composites and laminate composites, modelling difficulties and state-of-the-art modelling are outlined.
Abstract: The basic aspects of a damage mechanics approach for composites, capable of simulating complete fracture phenomena, are presented. First, for two material examples, ceramic composites and laminate composites, modelling difficulties and state-of-art modelling are outlined. Damage models with delay effects combined with a dynamic analysis are then introduced. Their possibilities are illustrated on one-dimensional bar problems. More complex examples, computed with a F. E. code specific to laminate damage analysis, are also highligted.
95 citations
TL;DR: In this article, a non-linear stress resultant four node shell finite element is presented and the underlying shell theory is developed from the three dimensional continuum theory via standard assumptions on the displacement field.
Abstract: A simple non-linear stress resultant four node shell finite element is presented. The underlying shell theory is developed from the three dimensional continuum theory via standard assumptions on the displacement field. A model for thin shells is obtained by approximating terms describing the shell geometry. In this work the rotation of the shell director is parameterized by the two Euler angles, although other approaches can be easily accomodated. A procedure is provided to extend the presented approach by including the through-thickness variable material properties. These may include a general non-linear elastic material with varied degree of orthotropy, which is typical for fibre reinforced composites. Thus a simple and efficient model suitable for analysis of multilayered composite shells is attained. Shell kinematics is consistently linearized, leading to the Newton-Raphson numerical procedure, which preserves quadratic rate of asymptotic convergence. A range of linear and non-linear tests is provided and compared with available solutions to illustrate the approach.
91 citations
TL;DR: In this paper, it was shown that hypersingular boundary integral equations may have an additional free term which has been erroneously omitted in former analyses, which is known as the free term of the hypersingularity.
Abstract: In this paper it is shown that hypersingular boundary integral equations may have an additional free term which has been erroneously omitted in former analyses.
77 citations
TL;DR: In this paper, the dual boundary element method is applied for the two-dimensional linear elastic analysis of fatigue problem of multiple-cracked body and the traction integral equation is applied on ones of surfaces of cracks while the usual displacement integral equation simultaneously on the others.
Abstract: The dual boundary element method is applied for the two-dimensional linear elastic analysis of fatigue problem of multiple-cracked body. The traction integral equation is applied on ones of surfaces of cracks while the usual displacement integral equation simultaneously on the others. General multiple crack growth problem is solved in a single-region formulation. All crack surfaces are discretized with discontinuous quadratic boundary elements. J-integral technique is used to evaluate stress intensity factors. The real extension path of cracks is simulated by a linear incremental crack extension, based on the maximum principal stress criterion. For each increment analysis of the cracks, crack extension is conveniently modelled with new boundary elements. Remeshing is no longer necessary. Fatigue life analysis is carried out with Paris' formulae. Several numerical examples show high efficiency of present method.
TL;DR: In this paper, a tensor product, wavelet-based finite element is constructed by employing the solution of an algebraic eigenvalue problem derived from the dyadic refinement equation characterizing the wavelet.
Abstract: This paper develops a class of finite elements for compactly supported, shift-invariant functions that satisfy a dyadic refinement equation. Commonly referred to as wavelets, these basis functions have been shown to be remarkably well-suited for integral operator compression, but somewhat more difficult to employ for the representation of arbitrary boundary conditions in the solution of partial differential equations. The current paper extends recent results for treating periodized partial differential equations on unbounded domains in Rn, and enables the solution of Neumann and Dirichlet variational boundary value problems on a class of bounded domains. Tensor product, wavelet-based finite elements are constructed. The construction of the wavelet-based finite elements is achieved by employing the solution of an algebraic eigenvalue problem derived from the dyadic refinement equation characterizing the wavelet, from normalization conditions arising from moment equations satisfied by the wavelet, and from dyadic refinement relations satisfied by the elemental domain. The resulting finite elements can be viewed as generalizations of the connection coefficients employed in the wavelet expansion of periodic differential operators. While the construction carried out in this paper considers only the orthonormal wavelet system derived by Daubechies, the technique is equally applicable for the generation of tensor product elements derived from Coifman wavelets, or any other orthonormal compactly supported wavelet system with polynomial reproducing properties.
TL;DR: In this article, the virtual crack closure integral method was used to calculate the stress intensity factors of an interfacial crack in a finite element model, and the results showed that the fracture criterion was less sensitive to the changes in characteristic length than fracture criterion based on the total energy release rate along with the phase angle.
Abstract: This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.
TL;DR: In this paper, a class of mixed finite element methods for Reissner-Mindlin plates proposed by Arnold and Brezzi is considered, where the shear energy term is split into two terms, leading to a partial selective reduced integration scheme.
Abstract: A class of mixed finite element methods for Reissner-Mindlin plates proposed by Arnold and Brezzi is considered. In these methods the shear energy term is split into two terms, leading to a partial selective reduced integration scheme. A parameter is involved in the splitting. In this paper an analysis of the behaviour of the approximate solution is performed in dependence of the parameter. Suggestions for a good choice of the parameter are also provided.
TL;DR: In this article, a range of lower-order element formulations that can be applied to both elastic and elasto-plastic large-strain elements are described, which can be considered as either a co-rotational approach or a modified form of the Biot stress procedure.
Abstract: The paper describes a range of lower-order element formulations that can be applied to both elastic and elasto-plastic large-strain elements. For plane-strain analysis, this process involves four-noded quadrilaterals while the enhancements involve incompatible modes or enhanced strains. One particular new formulation can be considered as either a “co-rotational approach” or a modified form of “Biot stress procedure”.
TL;DR: In this paper, a boundary integral equation method is applied to the solutions of three dimensional piezoelectric solids based on the reciprocal relations, and a pair of boundary integral formulae are formulated for evaluation of the fields in the medium.
Abstract: A boundary integral equation method is applied to the solutions of three dimensional piezoelectric solids. Based on the reciprocal relations, a pair of boundary integral formulae were formulated for evaluation of the fields in the medium. The Green's functions and their first partial derivatives employed in the formulations are evaluated numerically from the line integral solutions derived from the Fourier transform. By constructing some augmented matrices, we show that the topic can be treated systematically as that in the uncoupled elastic and dielectric problems. In illustration, we present results for the internal fields of a spherical cavity in an infinite piezoelectric medium loaded by a uniform traction on its boundary. Two piezoelectric ceramics, PZT-6B and gallium arsenide, are considered in the calculations. Some comparisons are made with solutions of purely elastic solids and with our recent calculations based on the finite element method.
TL;DR: In this paper, two approaches have been used in finite element studies of discontinuities in fluid mechanics: discontinuity capture using suitable mesh adaptivity and discontinuity fitting by introduction of discontinuous shape functions in the formulation.
Abstract: Two approaches have been used in finite element studies of discontinuities (shocks) in fluid mechanics. These are discontinuity capture using suitable mesh adaptivity and discontinuity fitting by introduction of discontinuous shape functions in the formulation. Both procedures have been now used successfully in solid mechanics, but the paper discusses the particular advantages of the adaptive process. The causes of discontinuity in plastic failure are reviewed and differences from the analogous fluid mechanics problems are discussed.
TL;DR: In this paper, an inverse analysis method using hierarchical neural networks and computational mechanics is described for the quantitative non-destructive evaluation with the ultrasonic method, and the trained network is utilized to determine appropriate defect parameters from some measured dynamic responses of solid surface.
Abstract: This paper describes an inverse analysis method using hierarchical neural networks and computational mechanics, and its application to the quantitative nondestructive evaluation with the ultrasonic method. The present method consists of three subprocesses. First, by parametrically changing the location and size of a defect hidden in solid, elastic wave propagation in the solid is calculated with the dynamic finite element method. Second, the back-propagation neural network is trained using the calculated relationships between the defect parameters and the dynamic responses of solid surface. Finally, the trained network is utilized to determine appropriate defect parameters from some measured dynamic responses of solid surface. The accuracy and efficiency of the present method are discussed in detail through the identification of size and location of a defect hidden in solid.
TL;DR: In this paper, the effects of combined in-line and transverse oscillation of a cylinder in the "lock-in" range of frequency on the time history of the drag and lift are investigated at a Reynolds number of 100.
Abstract: A computational study of the two dimensional flow past an oscillating cylinder is carried out using vorticity and stream function as the dependent variables. With the use of a log-polar coordinate transformation, the nondimensional vorticity transport equations in a non-inertial frame attached to the cylinder are solved using the ADI and SLOR finite difference schemes. The effects of combined in-line and transverse oscillation of the cylinder in the “lock-in” range of frequency on the time history of the drag and lift are investigated at a Reynolds number of 100. In addition, the influence of position amplitude of the cylinder's transverse oscillation on the lock-in range of frequency, mean drag, amplitude of drag and maximum lift is studied. The time histories of drag and lift forces in the case of combined oscillation are compared with the cases of the cylinder oscillating in the in-line and transverse directions separately. The dominant frequency components in the drag and the lift variations are determined using a Fourier frequency analysis.
TL;DR: In this article, the equivalent transverse shear and in-plane moduli of honeycomb cellular structures were derived based upon a two scale method for the homogenization of periodic media.
Abstract: This paper evaluates the equivalent transverse shear and in-plane moduli of honeycomb cellular structures. The derivation is based upon a two scale method for the homogenization of periodic media. The equivalent two dimensional constitutive equations are evaluated analytically in terms of their geometry and material properties. The present results compare well with some of the existing analytical results obtained by conventional approaches and show the errors of some of the earlier results. The present method is a systemetic and rational technique for the homogenization of periodically inhomogeneous media. It allows us to derive the equivalent mechanical properties of honeybombs systemetically for the analysis and design of cellular structures of honeycomb. The structural efficiency of honeycombs will also be discussed.
TL;DR: In this article, a spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis.
Abstract: A spline wavelets element method that combines the versatility of the finite element method with the accuracy of spline functions approximation and the multiresolution strategy of wavelets is proposed for frame structures vibration analysis. Instead of exploring orthogonal wavelets for specific differential operators, the spline wavelets are applied directly in finite element implementation for general differential operators. Although lacking orthogonality, the “two-scale relations” of spline functions and its corresponding wavelets from multiresolution analysis are employed to facilitate the elemental matrices manipulation by constructing two transform matrices under the constraint of finite domain of elements. In the actual formulation, the segmental approach for spline functions is provided to simplify the computation, much as conventional finite element procedure does. The assembled system matrices at any resolution level are reusable for the furthur finer resolution improvement. The local approximation and hiararchy merits make the approach competitive especially for higher mode vibration analysis. Some examples are studied as verification and demonstration of the approach.
TL;DR: In this article, an inverse identification method is proposed to determine material parameters in the nonlinear range, which consists of a finite element based inversion scheme associated to an optimization procedure, and a sensitivity analysis is used in order to determine the gradient of the cost function, representing the difference between the measured and the calculated response, with respect to the material parameters to identify.
Abstract: Inverse problem theory is getting of an increasing importance in mechanical modelling as it brings a solution to the identification to rheological behaviour of materials in the nonlinear range. As a matter of fact, when using inverse identification, the problem of experimental tests interpretation associated to inhomogeneous deformation states is bypassed. This allows a more accurate material parameters determination compared to the direct identification. In this paper, an inverse identification method is proposed to determine material parameters in the nonlinear range. The algorithm developed consists of a finite element based inversion scheme associated to an optimization procedure. A sensitivity analysis is used in order to determine the gradient of the cost function, representing the difference between the measured and the calculated response, with respect to the material parameters to identify. This method is applied to the inverse identification of viscoplastic parameters entering in the constitutive function that describes the flow stress of an aluminium alloy, for large range of strain, strain rate and temperature.
TL;DR: In this paper, the authors apply the finite element method to represent and compute the crystal orientation distribution function over an explicit discretization of orientation space, and apply the incremental Lagrangian to simulate the texturing of FCC crystals under monotonic deformations.
Abstract: Conventional polycrystal modeling is based primarily upon the association of a material element with a representative aggregate of crystals. In this work we focus on an alternate class of polycrystal schemes developed by applying the finite element method to represent and compute the crystal orientation distribution function over an explicit discretization of orientation space. In particular, we extend the methodology applied previously to planar polycrystals, to the modeling of three dimensional polycrystals. Neo-Eulerian axis angle spaces, and specifically Rodrigues' parameter space, are preferred over the conventional Euler angle spaces for this purpose. Various Eulerian and Lagrangian finite element schemes are considered for the ODF conservation equation, stabilized with appropriate combinations of streamline and artificial diffusion to accommodate its hyperbolic nature. One such stabilized scheme, the incremental Lagrangian is applied to simulate the texturing of FCC crystals under monotonic deformations. Next, the finite element polycrystal scheme is employed to capture the development of spatial texture gradients in a bulk forming process. This involves coupled finite element analyses at two length scales: at the macroscopic scale of the deformation process, over a spatial discretization, and at the microstructural level over the discretized orientation space.
TL;DR: In this article, a symmetric BIE-BE formulation for nonlocal, gradient-dependent plasticity is developed and discussed on the basis of its variationally consistent discretization.
Abstract: A boundary integral equation (BIE) formulation and a boundary element (BE) method which confer symmetry to key operators are concisely described with reference to quasi-static plasticity. This formulation is based on the combined use of static and kinematic sources, on Galerkin weighted residual enforcement of integral equations for displacements and tractions along the boundary and for stresses in the potentially yielding domain and on space discretizations in terms of generalized variables in Prager's sense. Typical theoretical results of computational interest not available in conventional nonsymmetric BE methods are surveyed. The subjectivity (mesh-dependence) implied by material instability is illustrated by examples. As a remedy, a symmetric BIE-BE formulation for nonlocal, gradient-dependent plasticity is developed and discussed on the basis of its variationally consistent discretization.
TL;DR: In this article, a hybrid crack tip finite-element is used to determine the stress intensity factors for an interfacial crack between dissimilar anisotropic media, which is based on the application of the path-independent J integral to a linear combination of two solutions: the problem to be solved, and an auxiliary solution with a known singular solution.
Abstract: Using Beom and Atluri's complete eigen-function solutions for stresses and displacements near the tip of an interfacial crack between dissimilar anisotropic media, a hybrid crack tip finite-element is developed. This element, as well as a mutual integral method are used to determine the stress intensity factors for an interfacial crack between dissimilar anisotropic media. The hybrid element has, for its Galerkin basis functions, the eigen-function solutions for stresses and displacements embedded within it. The “mutual integral” approach is based on the application of the path-independent J integral to a linear combination of two solutions: one, the problem to be solved, and the second, an “auxiliary” solution with a known singular solution. A comparison with exact solutions is made to determine the accuracy and efficiency of both the methods in various mixed mode interfacial crack problems. The size of the hybrid element was found to have very little effect on the accuracy of the solution: an acceptable numerical solution can be obtained with a very coarse mesh by using a larger hybrid element. An equivalent domain integral method is used in the application of the “mutual” integral instead of the line integral method. It is shown that the calculated mutual integral is domain independent. Therefore, the mutual integral can be evaluated far away from the crack-tip where the finite element solution is more accurate. In addition, numerical examples are given to determine the stress intensity factors for a delamination crack in composite lap joints and at plate-stiffener interfaces.
TL;DR: In this article, an averaged flow model for the resin flow through a double porous fiber preform is derived, and a simulation program is developed which is capable of predicting the flow pattern and temperature distribution in the mold filling process.
Abstract: In this paper, we present a modeling and numerical simulation of a mold filling process in resin transfer molding/structural reaction injection molding utilizing the homogenization method. Conventionally, most of the mold filling analyses have been based on a macroscopic flow model utilizing Darcy's law. While Darcy's law is successful in describing the averaged flow field within the mold cavity packed with a porous fiber preform, it requires experiments to obtain the permeability tensor and is limited to the case of porous fiber preform-it can not be used to model the resin flow through a double porous fiber preform. In the current approach, the actual flow field is considered, to which the homogenization method is applied to obtain the averaged flow model. The advantages of the current approach are: parameters such as the permeability and effective heat conductivity of the impregnanted fiber preform can be calculated; the actual flow field as well as averaged flow field can be obtained; and the resin flow through a double porous fiber preform can be modelled. In the presentation, we first derive the averaged flow model for the resin flow through a porous fiber preform and compare it with that of other methods. Next, we extend the result to the case of double porous fiber preform. An averaged flow model for the resin flow through a double porous fiber preform is derived, and a simulation program is developed which is capable of predicting the flow pattern and temperature distribution in the mold filling process. Finally, an example of a three dimensional part is provided.
TL;DR: In this paper, two real matrices, which play an important role in representing the stress field, are proposed and shown to be an extension of the Dundurs parameters to the anisotropic bimaterial.
Abstract: Nondimensional parameters that are needed to describe the stress field in an anisotropic bimaterial with tractions prescribed on its boundary are investigated. Two real matrices, which play an important role in representing the stress field, are proposed. They are shown to be an extension of the Dundurs parameters to the anisotropic bimaterial. A general solution of the stress and displacement fields in an anisotropic bimaterial with a straight interface is also obtained by using the complex function theory. In particular, a complete solution for the stress and displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic elastic media, is also derived.
TL;DR: In this article, a computationally efficient method for the first order step-by-step limit analysis of space frames is presented, which is based on the generalized plastic node method, and the solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method.
Abstract: A computationally efficient method for the first order step-by-step limit analysis of space frames is presented. The incremental non-holonomic analysis is based on the generalized plastic node method. The non-linear yield surface is approximated by a multi-faceted surface, thus avoiding the iterative formulation at each load step. In order to prevent the occurrence of very small load steps a second internal and homothetic to the initial yield surface is implemented which creates a plastic zone for the activation of the plastic modes. This implementation reduces substantially the computational effort of the procedure without affecting the value of the final load. The solution of the linear equilibrium equation at each load step is obtained with the preconditioned conjugate gradient method. Special attention is paid to the fact that the overall stiffness matrix changes gradually with the successive formation of plastic nodes. The application of the conjugate gradient method is based on some recent developments on improved matrix handling techniques and efficient preconditioning strategies. A number of test problems have been performed which show the usefulness of the proposed approach and its superiority in respect to efficient direct methods of solution in both storage requirements and computing time.
TL;DR: In this article, an approximate method is presented to investigate the interlaminar stresses near the free edges of composite laminate plates that are subjected to a combined thermo-mechanical loading.
Abstract: An approximate method is presented to investigate the interlaminar stresses near the free edges of composite laminate plates that are subjected to a combined thermo-mechanical loading. The method is based upon admissible function representations of stresses which account for the effects of both the global mismatches and the local mismatches in two of the elastic properties, the Poisson's ratio and the coefficient of mutual influence. For this purpose, new thermo-mechanical mismatch terms are defined to reflect an effective deformation under the combined thermo-mechanical loading. Closed form solutions of all the stress components are sought by minimizing the complementary energy with respect to the unknown functions, in the stress representations, of the width coordinate. These unknown functions are determined by solving five ordinary differential equations along with a set of free edge boundary conditions, which allow complex as well as real roots for their exponential decaying rates. The resulting solutions satisfy the stress equilibrium and all of the boundary conditions exactly, but compatibility is met in a weak form. Numerical examples are given for several typical laminates, and are compared with previous results obtained by finite element and other approximate methods. It is found that the present approximate method yields interlaminar stress results in an efficient, fast and yet reliable way. It is also concluded that unlike some previous approximate methods, the current method is numerically robust and stable.
TL;DR: In this paper, a comparison between new and existing triangular finite elements based on the shell theory proposed by Juan Carlos Simo and co-workers is presented, with particular emphasis on the description of new triangles which show a promising behaviour for linear and non linear shell analysis.
Abstract: A comparison between new and existing triangular finite elements based on the shell theory proposed by Juan Carlos Simo and co-workers is presented. Particular emphasis is put on the description of new triangles which show a promising behaviour for linear and non linear shell analysis.