摘要:

AbstractPlate finite elements based on the generalized third‐order theory of Reddy and the first‐order shear deformation theory are analysed and compared on the basis of thick and thin plate modelling behaviour, distortion sensitivity, overall accuracy, reliability and efficiency. In particular, several four‐noded Reddy‐type elements and the nine‐noded Lagrangian and heterosis (Mindlin‐type) plate elements are analysed to assess their behaviour in bending, vibration and stability of isotropic and laminated composite plates. A four‐noded Reddy‐type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general‐purpose finit

ISSN:0029-5981    

DOI:10.1002/nme.1620330802

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA numerical approach is developed for the solution of problems of materials with extremely strong directions. Small deformations of a transversely isotropic linear elastic solid, reinforced by a single family of inextensible fibres, are considered. The kinematic constraint equations of incompressibility and inextensibility in the fibre direction lead to the appearance of an arbitrary hydrostatic pressure and an arbitrary tension stress in the constitutive equations. A Galerkin approach is used to discretize the virtual work and weak form of the constraint equations. Independent interpolation of the displacement, pressure and tension fields leads to a mixed system of equations, with characteristic zero‐diagonal terms. The assumption of plane stress conditions in the plane of the fibres results in a simplified displacement‐tension formulation, analogous to the primitive‐variable formulation of Stokes flow. A mixed penalty approximation is then employed to solve for displacement and tension stress fields. Computations are carried out using a biquadratic displacement element with discontinuous bilinear tension stress interpolation. The formulation is used to solve a number of simple beam problems and the results compared to closed‐form so

ISSN:0029-5981    

DOI:10.1002/nme.1620330803

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element. Such a matrix is as important as the elastic and geometric stiffness matrices. It can be used not only in an eigenvalue analysis for testing the zero energy modes of a finite element under initial loadings, but for calculating the element forces in a step‐by‐step non‐linear analysis. The two‐dimensional beam element presented in this paper serves as a vehicle to demonstrate the concept involved. The principle of virtual work in its updated Lagrangian form has been adopted as the method of formulation. Several examples are provided to illustrate the adequacy of the present a

ISSN:0029-5981    

DOI:10.1002/nme.1620330804

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe paper first presents the details of the development of a new six‐noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution effort is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herei

ISSN:0029-5981    

DOI:10.1002/nme.1620330805

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe paper presents a simple and practical method for the local error assessment In the finite element solution of fields in linear media governed by the Laplace equation. The local error is estimated for each node or element of the mesh model by applying the Green integration formula, with the error distribution being used for the adaptive mesh refinement. Several alternatives of the local error estimation algorithm are compared and numerical examples are given for a typical ‘L’‐section potential problem. These confirm the efficiency of the proposed m

ISSN:0029-5981    

DOI:10.1002/nme.1620330806

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAdjoint and direct differentiation methods are used to formulate design sensitivities for non‐linear constrained elastostatic systems. Variations of a general response functional are expressed in explicit form with respect to all design field variations, including shape. The response functional is expressed over the undeformed configuration; however, the displacement gradient is included so that field quantities that are defined over the deformed configuration, such as Cauchy stress, may be modelled. The finite element method is used to evaluate the sensitivities in an example proble

ISSN:0029-5981    

DOI:10.1002/nme.1620330807

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractBased on elastic wave motion theory and the superposition concept, a numerical model for wave scattering problems in infinite media due to P‐wave and SV‐wave incidences is presented in this paper. Since this model is based on a coupled system of finite and infinite elements for simulating wave propagation in infinite media, the complexity of geometry and the variability of material properties in the foundation can be realistically simulated. Through a systematic study of the characteristics of a plane harmonic P‐wave and SV‐wave incidences on a fixed boundary, the concept of stress increase factors and stress factors which can be used to calculate the generalized stresses on the wave input boundary due to the SV‐wave and P‐wave incidences is also proposed. The effects of incident wave mode, incident angle and Poisson's ratio in the foundation on the stress increase factors and the stress factors have been studied in detail. Finally, the proposed model has been applied to a half‐plane foundation and a semi‐circular canyon to calculate SV‐wave and P‐wave scattering problems. The numerical results obtained show good agreement with the theoretical results and Wong's

ISSN:0029-5981    

DOI:10.1002/nme.1620330808

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper presents ap‐version geometrically non‐linear formulation based on the total Lagrangian approach for a nine node three dimensional curved shell element. The element geometry is defined by the coordinates of the nodes located on its middle surface and nodal vectors describing the bottom and top surfaces of the element. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the element and in the transverse direction. The element approximation functions and the corresponding nodal variables are derived from the Lagrange family of interpolation functions. The resulting approximation functions and the nodal variables are hierarchical and the element displacement approximation ensuresC° continuity.The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete three dimensional stresses and strains are considered, hence the element is equally effective for very thin as well as extremely thick shells and plates.Incremental equations of equilibrium are derived and solved using the standard Newton–Raphson method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the present formulation. The results obtained from the present formulation are compared with those available in the lite

ISSN:0029-5981    

DOI:10.1002/nme.1620330809

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non‐linear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement‐dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine‐node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formul

ISSN:0029-5981    

DOI:10.1002/nme.1620330810

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractBased on the incremental non‐linear theory of solid bodies and the Hellinger‐Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto‐plastic analysis of plane problems. In solving non‐linear problems, the Newton‐Raphson method with arc‐length control is adopted to trace the post‐buckling response. The computational steps to calculate the elasto‐plastic stress increments at Gauss points in the elasto‐plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto‐plastic analysi

ISSN:0029-5981    

DOI:10.1002/nme.1620330811

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY