摘要:

AbstractA new numerical approach has been devised for performing accurate absorbing–emitting non‐scattering radiation calculations for Cartesian co‐ordinate based problems with one ordinate symmetry using only the solution plane formed by the other two ordinates. To accomplish this, the method makes use of ‘effective intensity rays’ which only exist and have meaning in the solution plane of the problem but which are made, through a special procedure, to contain the information of the third dimension. This novel procedure thus eliminates the problem of solid angles and greatly reduces both the complexity and computational expense involved in the solution of such problems. Yet it can do this without producing loss in accuracy. The approach is ultimately intended for use in combustion problems involving high temperatures and optically thin media. For verification purposes the method is applied to the problem of heat exchange in infinitely long rectangular enclosures and is found to give excellent results over a optical thickness range that includes the optically very

ISSN:0029-5981    

DOI:10.1002/nme.1620371802

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractAn isoparametric rectangular mixed finite element is developed for the analysis of hypars. The theory of shallow thin hyperbolic paraboloid shells is based on Kirchhoff–Love's hypothesis and a new functional is obtained using the Gâteaux differential. This functional is written in operator form and is shown to be a potential. Proper dynamic and geometric boundary conditions are obtained. Applying variational methods to this functional, the HYP9 finite element matrix is obtained in an explicit form. Since only first‐order derivatives occur in the functional, linear shape functions are used and aC0conforming shell element is presented. Variation of the thickness is also included into the formulation without spoiling the simplicity. The formulation is applicable to any boundary and loading condition. The HYP9 element has four nodes with nine Degrees Of Freedom (DOF) per node—three displacements, three inplane forces and two bending, one torsional moment (4 × 9). The performance of this simple, and elegant shell element, is verified by applying it to some test problems existing in the literature. Since the element matrix is obtained explicitly, there is an important save of comput

ISSN:0029-5981    

DOI:10.1002/nme.1620371803

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn this paper a local–global analysis technique is presented for the non‐linear analysis of shells of revolution with a localized material discontinuity in the form of a crack or a cutout. The local zone is modelled using two‐dimensional general shell elements. Axisymmetric shell elements with Fourier description in the circumferential direction are used away from this local zone. In contrast to the earlier work of the authors, the geometric non‐linearity is taken into account in the axisymmetric zone as well. The harmonic coupling in the axisymmetric zone is efficiently handled through the pseudo‐load approach. A special preconditioned conjugate gradient iterative method is employed in conjunction with the arc length method for achieving improved convergence and negotiating the limit points. The attractive features of this methodology are that the tangential stiffness matrix of the structure is never assembled and factorized and that most of the computations are simple matrix–vector multiplications which are carried out efficiently at the element level. Numerical examples are presented to demonstrate the applicability of

ISSN:0029-5981    

DOI:10.1002/nme.1620371804

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractA mixed finite element method is presented for geometrically and materially non‐linear analysis of anisotropic incompressible hyperelastic materials. An incremental iteractive total Lagrangian formulation is adopted. The nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations, with characteristic zero diagonal terms. Computations are carried out using a three‐dimensional linear displacement, constant pressure element. A mixed penalty approximation is then employed to eliminate the pressure variables at the element level. The anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions. To demonstrate the applicability of this formulation to model complex anisotropic problems, the inflation of a cut toroidal tube with helical fibre orientation is analy

ISSN:0029-5981    

DOI:10.1002/nme.1620371805

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractDomain composition, a recently described method for formulating continuum field problems, removes certain restrictions on the construction of finite element models such that it is possible to solve a finite element problem without using a global compatible mesh. The domain composition method couples or otherwise constrains meshes in local regions to obtain a solution equivalent to that produced by conventional finite element methods. In particular, the domain composition method enables finite element models to be formulated with overlapping elements. Several advantages come from this, including an ability to automatically generate a finite element model from a solid geometric model, an ability to use a variety of element types in a single finite element model and an ability to exactly match element boundaries to the local geometry. This paper shows in detail a finite element formulation of Poisson's equation using domain composition and presents certain key algorithms that incorporate the domain composition method into well‐established finite element procedure

ISSN:0029-5981    

DOI:10.1002/nme.1620371806

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper presents a new algorithm for evaluating the eigenvalues and their corresponding eigenvectors for large‐scale non‐linear eigensystems in structural dynamics. The algorithm is based on solving a sequence of algebraic eigenproblems and updating the parameter λ. The implicitly restarted Lanczos method had been determined to be well suited for solving the linear eigenproblems that arise in this context. A zero‐finder approach that uses rational interpolation to approximate the generalized eigenvalues has been developed to update λ.The methodology of the new algorithm developed here is designed to evaluate a subset of the parametrized non‐linear eigencurves at specific values of λ. Numerical experiments show that the new eigensolution technique is superior to existing approaches for large‐scale problems and competitive for small‐size problems. The main emphasis of this contribution is the derivation and analysis of this scheme for non‐linear structu

ISSN:0029-5981    

DOI:10.1002/nme.1620371807

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper describes a design procedure for metal forming processes by using the controllable subspace of the full system. The velocity profile of the moving die is designed using the reduced order system. The metal forming processes are simulated using non‐linear finite element methods based on the rigid viscoplastic flow formulation. The balanced model reduction technique is applied to reduce the full state space model to a reduced order model that retains the controllable subspace of the thermomechanical system. The linear quadratic regulator theory with output tracking is used as an off‐line design tool to design the die velocity schedule. The process design is carried out to maintain the strain rate of the critical portion of the billet at a desired value. The procedure for designing the process parameters is demonstrated using two case stud

ISSN:0029-5981    

DOI:10.1002/nme.1620371808

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractIn the past, most finite element algorithms on data‐parallel computers have been limited to structured problem domains. Here, we consider methods to generalize the finite element method on data‐parallel architectures to unstructured domains. A nodal assembly algorithm is described which effectively allows for both the generation of the sparse interaction matrix (coefficient matrix) and its solution via a preconditioned conjugate‐gradient type routine utilizing several polynomial preconditioners on the Connection Machine 200 (CM‐200). Jacobi preconditioning along with Neumann series and least‐squares polynomial preconditioners are presented and implemented are presented and implemented. Only the Jacobi preconditioner produces an improvement in the convergence time for the problems examined. Several irregular interprocessor communication protocols available on the CM‐200 are investigated in the solution portion of the algorithm, yielding differing performance characteristics. For one such protocol, sustained performance of over two‐hundred MFlops/s, is demonstrated for a test problem on a 512 processing element CM‐200 in slicewise mode. The results are discussed and conclusions are drawn concerning this finite el

ISSN:0029-5981    

DOI:10.1002/nme.1620371809

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis article proposes an implicit algorithm for time integration of the differential/algebraic equations of small‐deformation elastoplasticity in strain space. The algorithm employs a two‐step backwards differentiation formula and a standard operator‐split procedure. Second‐order accuracy and non‐linear stability are established under appropriate constitutive restrictions. The algorithm is implemented for the model ofJ2‐plasticity and numerical simulations are conducted that illustrate its applicability a

ISSN:0029-5981    

DOI:10.1002/nme.1620371810

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractAccorsi has recently proposed a general method for modelling microstructural material discontinuities in a finite element analysis. In this work, it is shown that his method can be significantly simplified. In particular, the transformation strain (eigenstrain) plays no role in his application. Numerical results based on the simplified equations with 8‐node and 9‐node isoparametric elements are presented for the same examples as in his papers. The accuracy of the results is examined in comparison with the solution obtained from a complex mesh mo

ISSN:0029-5981    

DOI:10.1002/nme.1620371811

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY