Showing papers on "Finite element limit analysis published in 1977"
01 Jan 1977
2,004 citations
TL;DR: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems and boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits as mentioned in this paper.
Abstract: The finite element method is now recognized as a general approximation process which is applicable to a variety of engineering problems—structural mechanics being only one of these. Boundary solution procedures have been introduced as an independent alternative which at times is more economical and possesses certain merits. In this survey of the field we show how such procedures can be utilized in conventional FEM context.
711 citations
TL;DR: In this paper, a simple and efficient finite element is introduced for plate bending applications, where Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration, and the element is surprisingly accurate.
Abstract: A simple and efficient finite element is introduced for plate bending applications. Bilinear displacement and rotation functions are employed in conjunction with selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is surprisingly accurate.
647 citations
TL;DR: In this article, the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle was studied and the optimal error bounds were proved, as well as a general analysis of nonconforming finite element method.
Abstract: The paper is devoted to the construction of finite element methods for 2nd order elliptic equations based on a primal hybrid variational principle. Optimal error bounds are proved. As a corollary, we obtain a general analysis of nonconforming finite element methods.
322 citations
211 citations
01 Jan 1977
178 citations
01 Dec 1977
TL;DR: In this article, a simple recursion technique is employed to generate the matrix representing the annular region, where all nodes are eliminated from the external element except those on its inner surface, so that the final matrix is no larger than that required to describe the region of interest.
Abstract: Electric- and magnetic-field problems with boundaries at infinity are treated in finite-element terms by constructing an element to model an extremely large annulus surrounding the region of interest. A simple recursion technique is employed to generate the matrix representing the annular region. All nodes are eliminated from the external element except those on its inner surface, so that the final matrix is no larger than that required to describe the region of interest only. The method is simpler to program and requires less computing effort than boundary-integral techniques. It has been tested by solving several 2-dimensional magnetostatic and electrostatic problems and comparing the results with analytic solutions. The method can be applied to any 2-dimensional field problem bounded by a large empty region in which the field satisfies Laplace's equation.
157 citations
150 citations
TL;DR: It is proved that the iterative method can produce a solution to the equations in O(N) arithmetical operations where N is the number of unknowns.
Abstract: An iterative method of multiple grid type is proposed for solving general finite element systems. It is proved that the method can produce a solution to the equations in O(N) arithmetical operations where N is the number of unknowns.
99 citations
TL;DR: A number of temporal procedures for solving the long-wave surface water equations using the finite element method in space are presented and analyzed in this article, where the analysis determines the stability of the schemes and the error in wave amplitude and phase that can be expected.
77 citations
TL;DR: In this paper, finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs and evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
Abstract: Several finite element schemes for analysis of seepage in porous elastic media, based on different spatial and temporal discretization, were implemented in computer programs. Their numerical performance is evaluated by comparison with the exact solution for Terzaghi's problem of one-dimensional consolidation.
Book•
15 Jan 1977Dissertation•
02 Nov 1977
TL;DR: In this article, a discretized description of the kinematics of kinematically indeterminate structures as given in the finite element method is however also a good starting point for the numerical treatment of the analysis of mechanisms.
Abstract: The development of the finite element method for the numerical analysis of the mechanical behaviour of structures has been directed at the calculation of the state of deformation and stress of kinematically determinate structures. The discretized description of the kinematics of kinematically indeterminate structures as given in the finite element method is however also a good starting point for the numerical treatment of the analysis of mechanisms. In the description of the kinematics of mechanisms the relations between deformations and displacements play a central role. For the calculation of the transfer functions of order one and two, being the basic information for the determination of velocity and acceleration, direct methods are presented, applicable to mechanisms consisting of undeformable links. The description is completed with the formulation of dynamics, kinetostatics and vibrations. For mechanisms consisting of deformable links an approximate method is given. The theory is applied to planar mechanisms. Examples demonstrate the use of the theory in kinematic, dynamic and kinetostatic problems.
TL;DR: In this article, an error estimate for an incremental finite element method for plasticity with hardening is presented, where stresses and displacements are approximated by piecewise constant and piecewise linear functions, respectively.
Abstract: We prove an error estimate for an incremental finite element method for plasticity with hardening. Stresses and displacements are approximated by piecewise constant and piecewise linear functions, respectively.
TL;DR: In this article, the effects of anisotropy and shear deformation on the accuracy and convergence of shear-flexible displacement finite element models are considered, and numerical results show the effect of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.
Abstract: Two aspects of the finite element analysis of mid-plane symmetrically laminated anisotropic plates are considered in this paper. The first pertains to exploiting the symmetries exhibited by anisotropic plates in their analysis. The second aspect pertains to the effects of anisotropy and shear deformation on the accuracy and convergence of shear-flexible displacement finite element models. Numerical results are presented which show the effects of increasing the order of approximating polynomials and of using derivatives of generalized displacements as nodal parameters.
TL;DR: In this paper, a Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analyzed from the standpoint of local stability and convergence, and the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant.
Abstract: A Galerkin finite element formulation of diffusion processes based on a diagonal capacity matrix is analysed from the standpoint of local stability and convergence. The theoretical analysis assumes that the conductance matrix is locally diagonally dominant, and it is shown that one can always construct a finite element network of linear triangles satisfying this condition. Time derivatives are replaced by finite differences, leading to a mixed explicit-implicit system of algebraic equations which can be efficiently solved by a point iterative technique. In this work the accelerated point iterative method is adopted and is shown to converge when the conductance matrix is locally diagonally dominant. Several examples are included in Part II of this paper to demonstrate the efficiency of the new approach.
TL;DR: A combination of related techniques is proposed to make dynamic node distribution a useful tool within the framework of large-scale finite element analysis and to lead to improved grids in accord with engineering intuition.
TL;DR: Three main computing aspects encountered in the stress and strain analysis of the intact heart using the finite element technique, namely, the automatic partitioning of the myocardium of the heart into finite elements, the assemblage of the structural stiffness matrix of theMyocardium, and the storage and retrieval of its nonzero coefficients are described.
TL;DR: It is demonstrated that methods can readily be applied to solve problems involving nonlinear Neumann boundary conditions in the problem of designing an optimum distributed parameter system.
TL;DR: In this paper, the stable explicit algorithm of Saul'ev is extended to the finite element heat conduction transient analysis, which can be applied to both finite difference and finite element analysis in any number of spatial dimensions.
TL;DR: In this paper, postbuckling analysis of uniform cantilever columns subjected to three types of loading, namely a concentrated tip load, a uniformly distributed load and a linearly varying load has been presented using the Galerkin Finite Element Method.
01 Oct 1977
TL;DR: The Finite Element Method of Weighted Residuals (FEM) and Weighted residuals (MWR) are considered as computational schemes in the problem of acoustic transmission in nonuniform ducts as mentioned in this paper.
Abstract: The Method of Weighted Residuals (MWR) and the Finite Element Method (FEM) are considered as computational schemes in the problem of acoustic transmission in nonuniform ducts. MWR is presented in an improved form which includes the interaction of acoustic modes (irrotational) and hydrodynamic modes (rotational). FEM is based on a weighted residuals formulation using eight noded isoparametric elements. Both are applicable to two-dimensional and axially symmetric problems. Calculations are made for several sample problems to demonstrate accuracy and relative efficiency. One test case has implications in the phenomenon of subsonic acoustic choking and it is found that a large transmission loss is not an automatic consequence of propagation against a high subsonic mean flow.
TL;DR: In this paper, a new stress finite element for analysis of shell structures of arbitrary geometry and loading has been introduced, and the purpose of the present paper is to demonstrate the versatility of the proposed element with respect to all kinds of shell structure.
01 Jan 1977
TL;DR: In this paper, a mixed finite element method for finding approximations of the displacement and moments in a thin elastic-perfectly plastic plate was considered and an error estimate for the moments was proved under some weak assumptions concerning the regularity of the exact solution.
Abstract: We consider a mixed finite element method for finding approximations of the displacement and moments in a thin elastic-perfectly plastic plate. Under some weak assumptions concerning the regularity of the exact solution, we prove an error estimate for the moments. 1. Introduction. The purpose of this note is to prove an error estimate for a finite element method for thin elastic-perfectly plastic plates in the case of Hencky's law of plasticity. We shall consider a mixed finite element method, introduced by Herrmann (5) and Hellan (4), based on a piece wise constant approximation of the moments and piecewise linear approximation of the displacements. An analysis of this method, in the case of elastic plates, can be found in Brezzi and Raviart (1) and John- son (6). The results of this note can be extended to the case of quasi-static evolution following the argument in Johnson (8). For numerical results and practical experience of this method, we refer to Backhand (2).
TL;DR: Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various nonlinear and/or time-dependent problems in structural mechanics as discussed by the authors.
Abstract: Based on the Lagrange multiplier's concept, a superposition method of analytical and finite element solutions has been developed to solve efficiently various non-linear and/or time-dependent problems in structural mechanics. According to the theory, the transient creep behaviour of a cantilever beam is analysed as an expository example.