摘要:

AbstractThis paper presents an improved optimality criteria (OC) method for minimum‐weight design of bar structures supporting non‐structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to ‘adaptively’ tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is descreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrat the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesig

ISSN:0029-5981    

DOI:10.1002/nme.1620320102

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA refined global‐local method was proposed to improve the efficiency of finite element analysis. The proposed method was based on the regular finite element method in conjunction with three basic step, i.e. the global analysis, the local analysis and the refined global analysis. In the first two steps, a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest. These local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses. In the third step, a new global displacement distribution based on the results of the previous two steps was assumed for the analysis, from which much improved solutions for both stresses and displacements were produced. Numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method. Further, this method is suitable for parallel computatio

ISSN:0029-5981    

DOI:10.1002/nme.1620320103

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe paper presents results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods1have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.

ISSN:0029-5981    

DOI:10.1002/nme.1620320104

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe application of the Trefftz method for calculating wave forces on offshore structures is presented. Indirect and direct formulations using complete and non‐singular systems of Trefftz functions for the Helmholtz equation are posed in this paper. An effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force. The numerical examples show that the present method is highly efficient and accurat

ISSN:0029-5981    

DOI:10.1002/nme.1620320105

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractIssues related to the constitutive modelling and computational treatment of strain localization are examined for the class of rate independent solids. The significance of the constitutive description in localization problems is emphasized and constitutive models currently employed are briefly reviewed. Difficulties faced in finite element analysis, fundamentally associated with the loss of ellipticity of the related boundary value problem, and present trends in the computational treatment are discussed and illustrated by numerical examples.

ISSN:0029-5981    

DOI:10.1002/nme.1620320106

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA new approach to enforce surface contact conditions in transient non‐linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss‐Seidel method in which non‐linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also inc

ISSN:0029-5981    

DOI:10.1002/nme.1620320107

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractSampling points and weighting coefficients of the Gaussian type are presented for integrands typically encountered in axisymmetric finite elements. The proposed method is a generalization ofGaussian Integration of Momentsfor non‐zero limits of integration. The method achieves one extra order of accuracy in the integration of polynomials as compared with the Gauss‐Legendre method with the same number of sampling points. Although the locations of sampling points require the solution of non‐linear equations, analytical solutions are presented for the cases of one and two sampling points. Special cases of these general expressions are shown to include bothGauss‐Legendreintegration corresponding to an integration range at a considerable distance from the axis of symmetry, andFishmanintegration corresponding to an integration range whose lower limit lies on the axis of s

ISSN:0029-5981    

DOI:10.1002/nme.1620320108

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThis paper discusses the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of theC1deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.

ISSN:0029-5981    

DOI:10.1002/nme.1620320109

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThe study of the deviation of a crack reaching the interface separating two materials in a multilayer in a 4‐point deflection is considered. This study is based on the use of special isoparametric finite elements.1(The elements surrounding the crack tip have nodes placed at a distance α from the crack tip, and in this way we impose a singularity of the stresses in the neighbourhood of the crack.)The Erdogan2criterion that estimates the deviation angle shows that this angle is a function of the initial angle of the crack, and the properties of each component of the multilay

ISSN:0029-5981    

DOI:10.1002/nme.1620320110

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA fast algorithm is presented for constructing continuous lines, made up of element sides, which pass once through each node of a general unstructured triangular mesh and which are generally aligned in prescribed directions. The lines are used as the basis of an adaptive fully implicit unstructured grid procedure for the solution of two‐dimensional problems of steady compressible inviscid and laminar viscous high‐speed flows, where the equation system is solved by line relaxation using a block tridiagonal equation solver. For three‐dimensional laminar viscous simulations it is proposed to utilize an implicit/explicit finite‐element formulation. In the vicinity of solid walls a grid exhibiting structure in the normal direction is employed while, away from this region, the grid will be totally unstructured. In the structured region, lines in the normal direction to the wall are readily identified, while lines in the surfaces parallel to the solid wall are constructed using the proposed two‐dimensional procedure. The implicit algorithm is then used in the structured region and the equation solution is achieved via line relaxation. An explicit form of the solution algorithm is used elsewhere. To illustrate the performance of the proposed method, solutions are obtained for both transonic inviscid and transonic and hypersonic laminar viscous problems in two dimensions. The application of the proposed procedure to the solution of three‐dimensional hypersonic laminar viscous flow over a double ellipsoid configuration is als

ISSN:0029-5981    

DOI:10.1002/nme.1620320111

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY