摘要:

AbstractA family of stable algorithms for integration in time of the spatially discretized generalized Boussinesq equation is presented. In space, the finite element approximation is employed enabling arbitrary layout and variable physical properties. Furthermore, the proposed spatial–temporal discretization neither involves inversion of non‐diagonal matrices of large scale nor even their storage. The method is theoretically investigated and numerically tested. Comparison is made with known resu

ISSN:0029-5981    

DOI:10.1002/nme.1620211202

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe shear locking problem for the bilinear degenerated thick shell elements, when used in the context of thin shell structures, can be overcome by a generalized displacement method presented in this paper. The transverse shear energy in the degenerated thick shell elements is totally suppressed by introducing discrete Kirchhoff constraints in each element. The constrained variational problem based on the nodal displacement space is transformed into an unconstrained one based on a so‐called generalized displacement subspace. It is shown that shear looking phenomena completely disappear and no degradation of results is observed as the ratio of thickness to span approaches zer

ISSN:0029-5981    

DOI:10.1002/nme.1620211203

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractWe present a method which makes it possible to apply the idea of iterated defect correction to finite difference methods for the numerical treatment of partial differential equations. The method yields numerical approximations of very high accuracy for the solution, while the corresponding algebraic systems of equations still have ‘reasonable’ s

ISSN:0029-5981    

DOI:10.1002/nme.1620211204

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA mathematical programming approach is discussed for the finite element‐analysis of two‐phase undrained problems in the field of geomechanics. This approach enables us to account for the possible development of partially saturated zones in the geotechnical medium, due to the attainment of a given lower limit in the pore pressure distribution. Two alternative formulations are presented, both of them in terms of linear complementarity and quadratic programming problems, and the computational advantages of one of them are illustrated. The main characteristics of a step‐by‐step solution technique are presented. Finally, the solutions of some test problems are discussed and compared with those deriving from the traditional analyses in which the development of partial saturation is ne

ISSN:0029-5981    

DOI:10.1002/nme.1620211205

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe unilateral buckling of thin elastic plates, according to Kirchhoff's theory, is studied by using a boundary integral method. A representation for the second member of the equation is given. In the matrix formulatiea, boundary unknowns are eliminated; therefore, the unilateral buckling problem reduces to compute the eigenvalues and the eigenvectors of a matrix depending on the contact zone with the rigid foundation. An iterative process allows this zone and the buckling load to be computed. The capacities of the proposed method are illustrated by four examples.

ISSN:0029-5981    

DOI:10.1002/nme.1620211206

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA higher‐order shear deformation theory is used to analyse laminated anisotropic composite plates for deflections, stresses, natural frequencies and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, and requires no shear correction coefficients. A displacement finite element model of the theory is developed, and applications of the element to bending, Vibration and stability of laminated plates are discussed. The present solutions are compared with those obtained using the classical plate theory and the three‐dimensional elasticity the

ISSN:0029-5981    

DOI:10.1002/nme.1620211207

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe problem treated is the integration of singular functions which arise in three‐dimensional isoparametric formulations of boundary integral equations. A Taylor expansion in the local parametric co‐ordinates is developed for the singular integrand, so allowing singular terms to be integrated in closed form, even for curved surface elements. The remainder integral obtained by subtracting out the worst singularities is integrated by repeated Gaussian quadrature.Two groups of tests are presented. First, the accuracy of the integrations has been checked for plane parallelograms (for which exact solutions have been developed) and for curved elements on a sphere. Secondly, results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems; zonal surface harmonics on a sphere and the capacitance of an ellipsoid. The agreement obtained with few degrees‐of‐freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical inte

ISSN:0029-5981    

DOI:10.1002/nme.1620211208

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractThe frequently used subincremental method has so far been based on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic–plastic behaviour and secondary creep is involved. The present paper proposes a nonlinear subincremental method applicable to general elastic–plastic–creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear‐approach for elastic–plastic behaviour and when secondary creep is present. It is also linear during step loadings and it becomes increasingly more nonlinear, the more creep hardening deformations dominate the behaviour. A wide range of structures are analysed and the results from both subincremental methods are compared; the nonlinear strategy increases the accuracy by a factor of typically 3–5 without affecting the computer time. Moreover, the implementation of the nonlinear method is extremely simple. The optimum number of substeps in each main step is found to be around 5. For such a choice, the advantage of using the subincremental method as compared to the more conventional solution technique, where only one type of time step is used, is a significant reduction in computer time without, in practice, affecting t

ISSN:0029-5981    

DOI:10.1002/nme.1620211209

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA method is proposed to approximate the solutions of a certain class of differential equations, linear or nonlinear, in two or three, dimensions, provided that the boundary conditions are given on a rectangle or a parallelepiped, respectively. For other boundary shapes the co‐ordinate system must be transformed to meet that requirement. As in illustration, an example is given for the solution of Poisson's equation in two dimensions with a constant heat source, giving the temperatures on the rectangle together with the heat‐flow distribution along its edges. The basis of the method is a Taylor‐series development around one point; the result is given in terms of as many partial derivatives in that point as is desired. A similar method has already been described by Small2for the ‘heat equation’ ∂θ/∂t= ∂2θ/∂x22. Compared with finite difference and finite element solutions, these methods have the advantage that the solution is continuous, whereas first and second derivatives such as heat fluxes are available at hardly any effort. The results are compared with those of the exact solution. Even if the size of the determinant is limited to 4 × 4, the accuracy is already better than 98.98 per cent. When more effort is spent to solve a system of 10 equations, the accuracy is better

ISSN:0029-5981    

DOI:10.1002/nme.1620211210

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY

摘要:

AbstractA software system for the automated computer simulation of two‐dimensional elastostatic problems by the finite element method is described. This system consists of two parts, automated mesh generation and automated stress analysis. The mesh generation is based on a method in which equilateral triangles are generated successively in the unmeshed region. Automated mesh refinement is carried out in the latter part of the simulation process. The stress analysis is based on the assumed stress hybrid method and the successive over relaxation method. The computer program developed for this paper can generate a succession of increasingly refined triangular meshes until a certain mesh convergence criterion is achieved. The mesh convergence criterion is based on a comparison of nodal stresses in successive analyses until all the stress differences are within a specified toleranc

ISSN:0029-5981    

DOI:10.1002/nme.1620211211

出版商:John Wiley&Sons, Ltd    

年代:1985

数据来源: WILEY