Showing papers on "Smoothed finite element method 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
577 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
Book•
01 Feb 1977
TL;DR: Finite element techniques for fluid flow, Finite element techniques with real-time application, اطلاعات رسانی کشاورزی, £20,000 (US$30,000; €40,000)
Abstract: Finite element techniques for fluid flow , Finite element techniques for fluid flow , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی
226 citations
211 citations
01 Jan 1977
178 citations
TL;DR: In this paper, the nonisothermal finite strain dynamics of a porous solid containing a viscous fluid is developed on the basis of a new thermodynamics of open systems and irreversible processes.
TL;DR: In this article, mixed-hybrid finite element approximations are described for second-order elliptic boundary value problems, in which independent approximation methods are used for the solution and its gradient on the interior of an element and the trace of the gradients on the boundary of the element.
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.
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.
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 paper, numerical analysis of incompressible viscoelastic fluid flow is discussed using mixed finite element Galerkin method, which is assumed as the constitutive equation, stress components could not be eliminated from the governing equation system.
01 Jan 1977
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.
01 Jan 1977
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.
01 Jan 1977
TL;DR: In this paper, the effect of different mathematical formulations of the basic problem upon the results, the influence of the desired accuracy on the efficiency of the process, the selection and comparison of different types of elements, and, for nonlinear problems, the choice of efficient methods for solving the resulting finite dimensional equations.
Abstract: Present programs for finite element analysis require the user to make numerous, critical, a-priori decisions. They often represent difficult mathematical problems and may influence strongly the accuracy and reliability of the results, the cost of the computation, and other related factors. This paper discusses some of these decisions and their mathematical aspects in the case of several typical examples. More specifically, the questions addressed here concern the effect of different mathematical formulations of the basic problem upon the results, the influence of the desired accuracy on the efficiency of the process, the selection and comparison of different types of elements, and, for nonlinear problems, the choice of efficient methods for solving the resulting finite dimensional equations. In all cases a consistent use of self-adaptive techniques is strongly indicated.