Showing papers in "International Journal for Numerical Methods in Engineering in 1987"
TL;DR: In this article, a new method for non-linear programming in general and structural optimization in particular is presented, in which a strictly convex approximating subproblem is generated and solved.
Abstract: A new method for non-linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controlled by so called ‘moving asymptotes’, which may both stabilize and speed up the convergence of the general process.
4,218 citations
TL;DR: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
Abstract: A new error estimator is presented which is not only reasonably accurate but whose evaluation is computationally so simple that it can be readily implemented in existing finite element codes.
The estimator allows the global energy norm error to be well estmated and alos gives a good evaluation of local errors. It can thus be combined with a full adaptive process of refinement or, more simply, provide guidance for mesh redesign which allows the user to obtain a desired accuracy with one or two trials.
When combined with an automatic mesh generator a very efficient guidance process to analysis is avaiable.
Estimates other than the energy norm have successfully been applied giving, for instance, a predetermined accuracy of stresses.
2,449 citations
TL;DR: A new third degree polynomial transformation is found greatly to improve the accuracy of Gaussian quadrature scheme's within the near-singularity range and can easily be implemented into existing BE codes and presents the important feature of being self-adaptive.
Abstract: Almost all general purpose boundary element computer packages include a curved geometry modelling capability. Thus, numerical quadrature schemes play an important role in the efficiency of programming the technique. The present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two-dimensional, axisymmetric and three-dimensional applications. Emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of Gaussian quadrature scheme's within the near-singularity range. The procedure can easily be implemented into existing BE codes and presents the important feature of being self-adaptive, i.e. it produces a variable lumping of the Gauss stations toward the singularity, depending on the minimum distance from the source point to the element. The self-adaptiveness of the scheme also makes it inactive when not useful (large source distances) which makes it very safe for general usage.
666 citations
TL;DR: In this paper, an enthalpy formulation for convection/diffusion phase change is developed, where latent heat effects are isolated in a source term, and three alternative schemes for achieving this are presented.
Abstract: An enthalpy formulation for convection/diffusion phase change is developed. The essential feature of this formulation is that latent heat effects are isolated in a source term. This formulation is applicable to a general convection/diffusion phase change, i.e. it is valid in the cases of evolution of latent heat either at an isothermal temperature or over a temperature range. Before implementation of the enthalpy formulation, a technique is required to ensure that velocities predicted to be in a solid region actually take the value zero. Three alternative schemes for achieving this are presented.
The enthalpy formulation and velocity correction schemes are independent of the numerical technique. As an example of how the method can be implemented a control volume numerical discretization is chosen. This implementation is applied to two test problems: a solidification phase change in a cavity under conduction and the same phase change under conduction and natural convection. The natural convection problem is used to compare the performances of the various velocity correction schemes. The results of the problems are in good agreement with available analytical solutions and previous numerical solutions.
539 citations
TL;DR: In this paper, an unconditionally stable algorithm for the numerical integration of elastoplastic pressure-dependent constitutive relations is analyzed in detail, and the application of the method to plane stress problems, in which the out-of-plane strain component is not defined kinematically, is discussed.
Abstract: An unconditionally stable algorithm for the numerical integration of elastoplastic pressure-dependent constitutive relations is analysed in detail in this paper. The application of the method to plane stress problems, in which the out-of-plane strain component is not defined kinematically, is discussed. The tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations. The algorithm is applied to Gurson's constitutive model, some one-dimensional problems are solved, and comparisons with exact solutions are made. The paper closes with a numerical study of the necking of an axi-symmetric specimen using Gurson's plasticity model to describe the constitutive behaviour of the material.
429 citations
382 citations
TL;DR: In this article, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a near-crack-tip field parameter, the vector Je-integral, and its variation along the front of an arbitrary three-dimensional crack in a structural component.
Abstract: SUMMARY In this paper, an equivalent domain integral (EDI) method and the attendant numerical algorithms arc presented for the computation of a near-crack-tip field parameter, the vector Je-integral, and its variation along the front of an arbitrary three-dimensional crack in a structural component. Account is taken of possible non-elastic strains present in the structure; in this case the near-tip Je-values may be significantly different from the far-field values Jf , especially under non-proportional loading.
310 citations
TL;DR: The algorithmic changes made do ensure the robustness of the approach, but introduce additional algorithmic difficulties, the solutions of which are also presented.
Abstract: A technical description of the algorithms employed in the modified quadtree mesh generator is given. Although the basis of the mesh generator is the same as the original version developed by Yerry and Shephard,1,2 the actual algorithms on which it is built have been entirely changed for the purpose of ensuring the robustness of the technique. As demonstrated in the paper the algorithmic changes made do ensure the robustness of the approach, but introduce additional algorithmic difficulties, the solutions of which are also presented. In addition to examples showing the capability of the mesh generator, the linear computational growth rate of the mesh generator is demonstrated.
242 citations
TL;DR: In this article, a new method for the direct computation of strongly singular integrals existing in the Cauchy principal value sense is presented, which can be usefully applied in the solution by the direct boundary element method of many different problems.
Abstract: This paper presents a new method for the direct computation of strongly singular integrals existing in the Cauchy principal value sense. It can be usefully applied in the solution by the direct boundary element method of many different problems. Initially, some considerations are provided in order to summarize the state-of-the-art on this issue. Then the features of the proposed method are reported. The procedure allows the direct calculation of Cauchy principal value integrals with first-order singularity and it is applicable even in advanced boundary element methods employing high-order elements. It requires only the use of standard Gaussian quadrature formulae plus the computation of a logarithmic term. Some examples show the effectiveness and efficiency of the procedure.
189 citations
174 citations
TL;DR: In this paper, mathematical and computational aspects of device modelling are treated, including the analytical model, discretizations, non-linear and linear systems of equations, and properties of the matrices involved are presented in a systematic way.
Abstract: In this paper mathematical and computational aspects of device modelling are treated. Four main subjects are discussed; the analytical model, the discretizations, the non-linear and the linear systems of equations. On the one hand the most commonly used numerical techniques are described; on the other hand several new techniques are presented. Noteworthy new techniques are the generalized upwind box scheme and the mixed variable approach. Aspects such as the choice of variables and the singularly perturbed nature of the problem are treated. Properties of the matrices involved are presented in a systematic way. Throughout the paper a standard one-dimensional diode is used to illustrate the concepts involved. Finally several realistic two-dimensional examples are given.
TL;DR: In this article, an energy-based approach similar to the Rayleigh-Ritz method is developed, from which a stochastic finite element technique is derived, and several one-and two-dimensional example problems are solved.
Abstract: Galerkin's method is applied to random operator equations. Appropriate Hilbert spaces are defined for random functions and solutions are projected into these spaces, allowing the first- and second-moment properties of the solution to be calculated. An equivalent energy-based approach similar to the Rayleigh–Ritz method is developed, from which a stochastic finite element technique is derived. Several one- and two-dimensional example problems are solved and the results discussed.
TL;DR: Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.
Abstract: Methods for generating Pareto optimal solutions to a multicriterion optimization problem are considered. The norm methods based on the scalarization of the original multicriterion problem by using the l-norm are discussed in a unified form and a parametrization suitable for different interactive design systems is suggested. In addition, an alternative approach which, instead of scalarization, reduces the dimension of the multicriterion problem is proposed. This is called the partial weighting method and it can beinterpreted as a generalization of the traditional scalarization technique where the weighted sum of the criteria is used as the objective function. The first of these two approaches (norm method) is very flexible from a designer's point of view and it can be applied also in non-convex cases to the determination of the Pareto optimal set whereas the latter (partial weighting method) is especially suitable for problems where the number of criteria is large. Throughout the article several illustrative truss examples are presented to augment the scanty collection of multicriterion problems treated in the literature of optimum structural design.
TL;DR: In this paper, the convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detail, and various ways of fitting the boundary conditions in the T-complete functions method are presented.
Abstract: The paper presents various ways of fitting the boundary conditions in the T-complete functions method. The authors point out the distinct advantages of the orthogonal collocation in comparison to the equidistant collocation and the integral fit. The convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detail.
TL;DR: A method of solving a fuzzy multi-objective structural optimization problem using ordinary single- objective programming techniques is presented.
Abstract: It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.
TL;DR: In this article, a simple formulation of a nine d.o.f plane triangle is achieved by the assumed-stress hybrid approach, and a particularly simple form of the element, herein called the CST Hybrid, appears to be the best performer.
Abstract: A simple formulation of a nine d.o.f plane triangle is achieved by the assumed-stress hybrid approach. The element has two translations and the rotation about a normal to the plane as d.o.f. at each node. Performance of the element is shown to be good. A device for softening overly-stiff elements is found to be effective and is suggested as a widely applicable method of improving the behaviour of hybrid elements. A particularly simple form of the element, herein called the CST Hybrid, appears to be the best performer.
TL;DR: In this paper, the p-method capabilities have thus far been used only in connection with the assumed displacement model elements, where singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity.
Abstract: The p-method capabilities have thus far been used only in connection with the assumed displacement model elements. When such elements are used, singular points have to be isolated by one or two layers of small elements graded in a suitable geometrical progression towards singularity. This paper presents an alternative formulation which circumvents this drawback and enables excellent solution results to be obtained with uniform FE-grids. The formulation is based on the recently presented hybrid-Trefftz FE-model and makes use of optional expansion sets for various singularities or stress concentrations. Stress concentrations due to concentrated loads are also properly accounted for. It is shown that by augmenting the order of approximation over a fixed grid of such elements rapid convergence towards the accurate solution is obtained in the most efficient way.
This paper summarizes the results of a preliminary study that had been undertaken to critically evaluate the potential of the new approach as a suitable basis for subsequent developments of a fully automated adaptive process.
TL;DR: In this article, a Petrov-Galerkin finite element method for two and three-dimensional time dependent convection-diffusion equations is presented in the context of two space dimensions.
Abstract: A Petrov—Galerkin finite element method for two and three-dimensional time dependent convection-diffusion equations is presented in the context of two space dimensions. The method involves perturbed weighting functions in the weighted residuals formulation, that are bilinear in space and quadratic in time and depend on two parameters which are calculated according to a local analysis for the one dimensional case. The perturbations to the weighting functions can be interpreted as an added local anisotropic balancing diffusion and an added dispersion in the direction of the convective motion. The effectiveness of the method is shown through several examples involving the convective and diffusive transport of scalar distributions in known velocity fields.
TL;DR: In this paper, an algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented, which solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective stress function: a functional relationship which involves only the effective stress.
Abstract: An algorithm for stable and accurate computations of stresses in finite element thermo-elastic-plastic and creep analysis of metals is presented. The effective-stress-function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective-stress-function: a functional relationship which involves as unknown only the effective stress. The derivation of the effective-stress-function for thermo-elasto-plasticity conditions, including creep, for 2-D and 3-D analysis is presented, and the algorithmic steps of the stress solution are discussed. For use in the stiffness matrix a tangent material stress–strain relationship is evaluated consistent with the effective-stress-function algorithm. The solution of some demonstrative problems shows the effectiveness of the solution procedure.
TL;DR: In this article, a new shell element, which is free from serious locking problems and which does not possess hourglass modes, is proposed, which exhibits good convergence for plates with variable thickness.
Abstract: A new shell element, which is free from serious locking problems and which does not possess hourglass modes, is proposed. Solutions obtained with this element exhibit good convergence and are satisfactorily insensitive to mesh distortion. The element also exhibits good convergence for plates with variable thickness. This element is based on the use of assumed covariant strains which are obtained from the covariant strain field defined with respect to the element natural co-ordinate system. Only the linear version for thin shell cases is considered. The element performance is tested by application to several standard plate and shell problems. A problem involving variable thickness is also presented.
TL;DR: In this paper, a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates, where the element formulation assumes transverse inextensibility and layerwise constant shear-angle.
Abstract: The development of a general triangular C0 element, based on an assumed quadratic displacement potential energy approach, is presented for the analysis of arbitrarily laminated thick plates. The element formulation assumes transverse inextensibility and layerwise constant shear-angle. Convergence of transverse displacement, moments and stresses, the effects of two different Gauss quadrature schemes and comparison of the present solutions with the available analytical/finite-element results also form a part of the investigation. Furthermore, numerical results indicate close agreement between the LCST (layerwise constant shear-angle theory) and the three-dimensional elasticity theory with the length (or width) to thickness ratio as low as 4. Detailed comparison of the LCST-based finite-element solutions with those based on the CST (constant shear-angle theory) and the CLT (classical lamination theory) clearly demonstrates the superiority of the former over the latter two, especially in the prediction of the distribution of the in-plane displacements and stresses through the laminate thickness. This paper also introduces a new non-dimensionalized parameter, Δθ*, which is shown to be a very useful measure for classification of the laminated plates and the suitability of different plate theories over various ranges of length-to-thickness ratio.
TL;DR: A procedure to generate 2D meshes of triangles in a quite general fashion allowing for local and selective mesh-refinement is presented and discussed.
Abstract: A procedure to generate 2D meshes of triangles in a quite general fashion allowing for local and selective mesh-refinement is presented and discussed. The grid generator is based on the iterative application of 4-triangles conforming mesh-refinement algorithms for triangulations, which are also introduced in this paper. These algorithms are modified versions of those proposed in Int. j. numer. methods eng., 20, 745–756 (1984), and they can be used for global refinement of a grid, as well as for local refinement. The grid generator works in the following way: given any initial coarse triangulation which properly defines the geometry of the problem, a set of user-defined refinement subregions Ri, i = 1,2,…, N, and an associated set of tolerance parameters hi, an irregular and conforming final triangulation is automatically constructed in such a way that the diameter of all the triangles contained in Ri is smaller than hi, i= 1,2,…, N. Moreover, all angles in the final triangulation are greater than or equal to half the smallest angle in the initial, coarse one. The refinement is propagated only to assure the conformity and smoothness of the grid, and consequently, the number of involved nodes will be minimized. The refinement of the final mesh will be determined by the subregions Ri and the parameters Ni and will be essentially independent of the initial coarse grid. The 4-triangles conforming mesh-refinement algorithms are presented and their properties discussed. The implementation of these techniques is discussed and examples of the application of the grid generator are given.
TL;DR: In this article, a finite element method was used to analyze the dynamic responses of a flat plate subjected to various moving loads, including eccentricity, acceleration and initial velocity of the moving load, and the effect of span length.
Abstract: SUMMARY The object of this paper is to analyse by the finite element method the dynamic responses of a flat plate subjected to various moving loads. First of all the actual continuous flat plate was replaced by a discrete system composed of isoparametric rectangular plate elements. And then the elementary and overall stiffness and mass matrices were determined and the natural frequencies and mode shapes of the flat plate were solved. Next, the Newmark direct integration method was used to find the dynamic responses of the flat plate. The effects of eccentricity, acceleration and initial velocity of the moving load, and the effect of span length were the key points of study. The dynamic behaviour of a multi-span flat plate supported by the beam members of rigid plane frames and subjected to the action of a series of moving loads (in identical or opposite directions) were also investigated.
TL;DR: In this article, a simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields.
Abstract: A simple, shear flexible, quadrilateral plate element is developed based on the Hellinger/Reissner mixed variational principle with independently assumed displacement and stress fields. The crucial point of the selection of appropriate stress parameters is emphasized in the formulation. For this purpose, a set of guidelines is formulated based on the follwoing considerations: (1) suppression of all kinematic deformation modes, (2) the element has a favorable value for the constraint index in the thin plate limit, and (3) element properties are frame-invariant. For computer implementation the components of the element stiffness matrix are evaluated analytically using the symbolic manipulation package MACSYMA. The effectiveness and practical usefulness of the proposed element are demonstrated by the numerical results of a variety of problems involving thin and moderately thick plates under different loading and support conditions.
TL;DR: A simple expert system frame is suggested and provides the domain knowledge for the optimal mesh design and the prediction of the error in energy norm for the problem of plane elasticity using the hp-extension in the finite element method.
Abstract: : This paper suggests a simple expert system frame and provides the domain knowledge for the optimal mesh design and the prediction of the error in energy norm for the problem of plane elasticity using the hp-extension in the finite element method. The expert system monitors the progress of the analysis, guides the user through the various steps and is able to reason about its own advise. In an example the user-expert communication is shown and the superiority of the results is demonstrated. The goals are the following: 1) The input data of the user should be kept to a minimum; 2) The user should get rational support for his decisions about the mesh design; 3) The system should be able to monitor the progress of the analysis; 4) It should advise the user at each time about the next steps to be taken; 5) The system should be able do reason about its own advise; 6) The expert system frame should be separated in a problem-independent part , the inference engine and the problem dependent knowledge base; and 7) A user should be achieved for given cost.
TL;DR: In this paper, a nine node shell element is developed by a new and more efficient mixed formulation, which is based on the Hellinger-Reissner principle with independent strain and the concept of degenerate solid shell.
Abstract: : A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger-Reissner principle with independent strain and the concept of degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower part and a higher order part. Numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable. In fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix.