Showing papers in "Computer Methods in Applied Mechanics and Engineering in 1976"

TL;DR: In this paper, a finite element method for a class of contact impact problems is presented, where the basic ideas of contact-impact, the assumptions which define the class of problems we deal with, spatial and temporal discretizations of the bodies involved, special problems concerning the contact of bodies of different dimensions, discrete impact and release conditions, and solution of the nonlinear algebraic problem are discussed.

TL;DR: In this article, two new schemes are introduced which reduce this error but retain the advantages of upstream differencing, which is particularly accurate in problems where diffusion and convection play dominant roles in establishing the distribution of the dependent variable.

TL;DR: In this paper, the authors show that the false diffusion normally associated with upstream differences is a poor indicator of the total error in approximating the convection terms, and a new definition for false diffusion is proposed.

TL;DR: In this article, a mode superposition technique for approximately solving nonlinear initial-boundary-value problems of structural dynamics is discussed, and results for examples involving large deformation are compared to those obtained with implicit direct integration methods such as the Newmark generalized acceleration and Houbolt backward difference operators.

TL;DR: In this paper, the singular integral equation (1.2) on a closed surface Γ of R3 admits a unique solution q and is variational and coercive in the Hilbert space H − 1 2 (Γ).

TL;DR: A general method in the form of an accelerated preconditioned iterative refinement method is presented for the solution of symmetric, sparse matrix problems, and some inherently advantageous properties of the conjugate gradient acceleration method are pointed out.

TL;DR: In this article, a method is described for the selection of cycle bases leading to sparse flexibility matrices for the analysis of skeletal structures, which is made by an expansion process and the use of Mayer-Vietoris additivity formula.

TL;DR: In this article, a numerical procedure for the analysis of general two-dimensional flows of viscous, incompressible fluids using the finite element method is developed, where the partial differential equations describing the continuum motion of the fluid are discretized by using an integral energy balance approach in conjunction with a finite element approximation.

TL;DR: This paper considers the use of unorthodox grids where rapid transition from refined zones to coarser zones is effected, thus introducing exposed nodal freedoms at the zone interfaces, and a technique for automated mesh enrichment of finite element discretizations is devised.

TL;DR: In this paper, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton, without any reference to the theory of differential equations.

TL;DR: In this paper, the classical variational principles are formulated for nonlinear problems by considering incremental deformations of a continuum and associated finite element models are derived, adopting the terminology introduced by Pian for classification of linear finite elements models.

TL;DR: In this paper, different types of symmetry exhibited by anisotropic shells for various loadings and boudary conditions are identified, and a simple procedure is presented for exploiting these symmetries in the finite element analysis.

TL;DR: In this paper, a nonconforming finite element, Wilson's element, for solving the elastic problem is mathematically studied and the errors on the stresses and displacements are shown to be asymptotically of order h and h 2, respectively, where h is the supremum of the lengths of the sides of the elements.

TL;DR: In this article, the duality concepts for linear elastic analysis by the finite element method are extended to the plasticity problem using classical variational principles; in this way, both primal and dual quasi-direct approaches to the limit analysis problem are identified.

TL;DR: In this paper, the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices is explored for a rectangular prestressed membrane element, and efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail.

TL;DR: In this article, the computational costs of some finite element and finite difference methods currently used to solve the shallow water equations are compared on theoretical grounds and it is shown that because band algorithms are employed, the finite element methods considered are not economically attractive for practical calculations.

TL;DR: In this article, a variational formulation applicable to linear operators with nonhomogeneous boundary conditions and jump discontinuities is presented, where operators on inner product spaces, convolution spaces and energy spaces are included as specializations.

TL;DR: In this article, a finite element formulation of the load domain of shakedown is proposed, where the static approach is utilized together with the yield criterion of the mean, and the assumptions on the discrete residual stress field are adopted exactly in the same manner as for elastic asymptotic stress fields in pure equilibrium elements which guarantee the total stress transmission to be perfectly continuous.

TL;DR: In this article, a general numerical procedure for the analysis of two-dimensional flows of viscous, incompressible fluids, using the finite element method, was described, and a number of special computational procedures were also discussed that allowed significant reductions to be made in the computational effort required in the solution of problems.

TL;DR: In this article, a constitutive model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure and upon intersection with the stress path the failure surface collapses for brittle behavior according to one of three softening rules.

TL;DR: In this article, a simple and practical test is presented and demonstrated for the evaluation of a finite element, referred to as a "single element test" (SET), which is used to evaluate the performance of finite elements.

TL;DR: In this article, a sophisticated finite element for elastic arches of arbitrary geometry and loading is developed, based on a mixed variational principle, and convergence of the method is proven and rates of convergence for stresses and displacements are established.

TL;DR: In this article, an extension of Prager's shakedown theorem to the general case of discrete structures and for a broader class of hardening rules, with temperature and geometric effects included, was given.

TL;DR: In this article, a theoretical analysis for the large deflection elastic behavior of clamped, uniformly loaded orthotropic skew plates is presented, where the governing nonlinear partial differential equations are transformed into a set of nonlinear algebraic equations.

TL;DR: In this paper, the applicability of linear programming is illustrated for single load conditions to safeguard against failures by yielding, buckling, and excessive deformations, while nonlinear programming is used as the design tool for multiple loading conditions.

TL;DR: In this article, the mechanical equations of an extensible, perfectly flexible curvilinear material (cable) are formulated and the static problem can be solved either by a minimization technique or by an iterative finite difference method which also permits dealing with forces that are not derived from a potential.

TL;DR: In this paper, a new type of iterative improvement is introduced where the residual is calculated in single precision, and the iteration scheme is analysed with respect to round-off errors and found to give significant improvement over existing direct approaches.

TL;DR: In this paper, a new formulation of the Householder-QR decomposition is given in terms of unitary Hermitian matrices generalizing the concept of an elementary unitary hermitian.