摘要:

AbstractAnalytical solutions for displacements and stresses in composite laminates are developed using the laminate plate theory of Reddy. The theory accounts for a desired degree of approximation of the displacements through the laminate thickness, allowing for piecewise approximation of the inplane deformation through individual laminae. The solutions are compared with the 3‐D elasticity solutions for the simply supported case and excellent agreement is found. Analytical solutions are also presented for other boundary conditions. The results indicate that the generalized shear deformation plate theory predicts accurate stress distributions in thick composite laminate

ISSN:0029-5981    

DOI:10.1002/nme.1620290103

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe field‐boundary‐element method naturally admits the solution algorithm in the incompressible regimes of fully developed plastic flow. This is not the case with the generally popular finite‐element method, without further modifications to the method such as reduced integration or a mixed method for treating the dilatational deformation. The analyses by the field‐boundary‐element method for geometric and material non‐linear problems are generally carried out by an incremental algorithm, where the velocities (or displacement increments) on the boundary are treated as the primary variables and aninitial strain iterationmethod is commonly used to obtain the state of equilibrium. For problems such as buckling and diffused tensile necking, involving very large strains, such a solution scheme may not be able to capture the bifurcation phenomena, or the convergence will be unacceptably slow when the post‐bifurcation behaviour needs to be analysed. To avoid this predicament, a full tangent stiffness field‐boundary‐element formulation which takes the initial stress–velocity gradient (displacement gradient) coupling terms accurately into account is presented in this paper. Here, the velocity field both inside and on the boundary are treated as primary variables. The large strain plasticity constitutive equation employed is based on an endochronic model of combined isotropic/kinematic hardening plasticity using the concepts of material director triad and the associated plastic spin. A generalized mid‐point radial return algorithm is presented for determining the objective increments of stress from the computed velocity gradients. Numerical results are presented for problems of diffuse necking, involving very large strains and plastic instability, ininitially perfectelastic–plastic plates under tension. These results demonstrate the clear superiority of the full tangent stiffness algorithm over the initial strain algorithm, in the context of the integral equation formulations for

ISSN:0029-5981    

DOI:10.1002/nme.1620290104

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractFully automatic three‐dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular—the octree and Delaunay approaches—have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide‐and‐conquer approach of the octree method with the simplicity and optimal properties of the Delaunay tria

ISSN:0029-5981    

DOI:10.1002/nme.1620290105

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractAxisymmetric contact problems of an elastic layer are studied in this paper. The lower surface of the layer is either bonded to or in smooth contact with a rigid base. The upper surface is in tensionless smooth contact with a rigid flat cylinder, a rigid sphere, an elastic sphere or a circular plate, respectively. A general method is developed so that all these related problems are treated in a straightforward and like manner. In comparison to the other methods used in previous papers, the simplicity and high numerical accuracy are the major advantages of this method. The convergence is proved by comparing the numerical values to some available analytical solutions. Extensive numerical results for contact radii, displacements and contact pressures are provided.

ISSN:0029-5981    

DOI:10.1002/nme.1620290106

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractIn this paper, a method for the non‐linear dynamic analysis of rectangular plates that undergo large rigid body motions and small elastic deformations is presented. The large rigid body displacement of the plate is defined by the translation and rotation of a selected plate reference. The small elastic deformation of the midplane is defined in the plate co‐ordinate system using the assumptions of the classical theories of plates. Non‐linear terms that represent the dynamic coupling between the rigid body displacement and the elastic deformation are presented in a closed form in terms of a set of time‐invariant scalars and matrices that depend on the assumed displacement field of the plate. In this paper, the case of simple two‐parameter screw displacement, where the rigid body translation and rotation of the plate reference are, respectively, along and about an axis fixed in space, is first considered. The non‐linear dynamic equations that govern the most general and arbitrary motion of the plate are also presented and both lumped and consistent mass formulations are discussed. The non‐linear dynamic formulation presented in this paper can be used to develop a total Lagrangian finite element formulation for plates in multibody systems consisting of interconnected struct

ISSN:0029-5981    

DOI:10.1002/nme.1620290107

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe paper compares the overall performance of a wide range of numerical procedures that can be used to integrate through the thickness of plates and shells. Results are presented for the accuracy of the calculations when there are discontinuities in the stress through the depth of the plate, and the available methods are ranked according to their accuracy.

ISSN:0029-5981    

DOI:10.1002/nme.1620290108

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractIn this paper there is presented an alternative numerical procedure for obtaining approximations to non‐linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress–strain relation is non‐linear). The above‐mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic‐non‐linear rod, fixed at its edges, that is left in a non‐equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed

ISSN:0029-5981    

DOI:10.1002/nme.1620290109

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right‐hand sides. The versions of the method proposed in the past treat the right‐hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vect

ISSN:0029-5981    

DOI:10.1002/nme.1620290110

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThe complex variable boundary element method (CVBEM) developed by Hromadka for the solution of potential problems in simply connected domains is extended to the solution of heat conduction problems in doubly connected domains. A cut is made in the doubly connected domain, and it was found that the complex potentials along the cut do not cancel out but result in a complex stream function that plays the role of perturbation in the nodal equations. Cauchy–Riemann conditions are used to derive additional equations which relate the stream functions and the boundary heat fluxes and potentials when Neumann and Robin conditions are imposed on the boundaries. The resulting nodal equations are expressed in matrix form, and coding rules and methods for checking the matrix elements are developed. Three solution methods (implicit, explicit and hybrid) are described, and by means of examples, the efficacy of these methods is discussed and compare

ISSN:0029-5981    

DOI:10.1002/nme.1620290111

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractThermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermo‐elasto‐plastic behaviour of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with non‐zero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress resp

ISSN:0029-5981    

DOI:10.1002/nme.1620290112

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY