Showing papers on "Smoothed finite element method published in 1975"
TL;DR: The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon as discussed by the authors, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
Abstract: Introduction to finite element analysis: 1.1 What is ... The finite element method (FEM) is a numerical technique used to perform finite element analysis of any given physical phenomenon. It is necessary to use mathematics to comprehensively understand and quantify any physical phenomena, such as structural or fluid behavior, thermal transport, wave propagation, and the growth of biological cells.
1,811 citations
01 Oct 1975
TL;DR: An application for a one-dimensional long period shallow water wave using he method of Galerkin an the four-step Runge-Kuta method is described in this article. But the application is limited to a single wave.
Abstract: An application for a one-dimensional long period shallow water wave using he method of Galerkin an the four-step Runge-Kuta method.
147 citations
Book•
01 Jan 1975
TL;DR: In this article, the authors present a structural analysis of a Continuum Mechanics Problem with Finite Element Analysis of Harmonic Problems and finite element analysis of Biharmonic Problems.
Abstract: Introduction and Structural Analysis Continuum Mechanics Problems Finite Element Analysis of Harmonic Problems Finite Element Meshes Some Harmonic Problems Finite Element Analysis of Biharmonic Problems Some Biharmonic Problems Further Applications.
108 citations
TL;DR: In this paper, a curved-shell finite element of triangular shape is described which is based on conventional shell theory expressed in terms of surface coordinates and displacements Each of the three surface displacement components is independently represented by a two-dimensional polynomial of constrained-quintic order giving the element a total of 54 degrees of freedom.
55 citations
TL;DR: In this article, the finite element method was applied to the radially symmetric case of the hydrogen atom, which has computational advantages over the finite difference and Rayleigh−Ritz methods.
Abstract: The finite element method, which in other fields has replaced finite difference and variational methods, is applied to the radially symmetric case of the hydrogen atom. The method is shown to have computational advantages over the finite difference and Rayleigh−Ritz methods. (AIP)
46 citations
45 citations
Proceedings Article•
01 Jan 1975
41 citations
TL;DR: A study of the constraint of incompressibility in the finite element method for plane strain through the use of a Lagrange multiplier and its two approaches from the point of view of rate of convergence and computer time is presented.
Abstract: The constraint of incompressibility is incorporated into the finite element method for plane strain through the use of a Lagrange multiplier. Depending on the approximating function chosen for this multiplier, the constraint condition can be satisfied everywhere within the element or only in an average sense for the entire element. A study of these two approaches from the point of view of rate of convergence and computer time is presented.
37 citations
33 citations
TL;DR: In this article, a higher order beam finite element is derived and shown to be very efficient in solving the transient dynamic problem of elastic impact and impact with permanent indentations, and the finite element solutions are found in good agreement with some existing solutions.
TL;DR: A review of developments in the finite element field can be found in this article, where the concept of stiffness analysis is introduced and a review of recent developments in finite element fields is presented.
Abstract: Basic concepts The concept of stiffness analysis Bar finite elements Finite elements of continua Triangular finite element for plane elasticity Rectangular finite element for plane elasticity Rectangular finite element for plate flexure Analysis of folded-plate, box-girder and shell structures using rectangular elements Axially symmetric continua Programming Triangular finite element for plate fixture A review of developments in the finite element field Appendices.
TL;DR: In this article, finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids, and the particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty.
Abstract: Finite element methods are used to solve hydrodynamic lubrication problems involving compressible lubricants and porous bearing solids. The particular calculation scheme permits solution at high compressibility numbers (Λ > 100) to be obtained without any numerical difficulty. Finite element and finite difference results for the porous, gas lubricated journal bearing are presented and compared.
TL;DR: In this paper, differential equation descriptions for specific three-dimensional environmental hydrodynamical flowfields are established and a finite element numerical solution algorithm is established for each of these developed systems including complete nonlinearity and tensor turbulent transport phenomena.
Abstract: Differential equation descriptions for specific three-dimensional environmental hydrodynamical flowfields are established. The parabolic Navier-Stokes system is applicable to predominant direction steady flowfields. An integral transform formulation of the transient Navier-Stokes system is applicable to recirculating flowfields in lakes, rivers, and tide water regions. A finite element numerical solution algorithm is established for each of these developed systems including complete nonlinearity and tensor turbulent transport phenomena. The algorithm directly utilizes nonuniform computational meshes and nonregular solution domain closures, upon which boundary condition constraints may be readily applied.
01 Jan 1975
TL;DR: In this paper, discrete equations are formed by applying Ampere's circuital law around each node, and a variational formulation for transient conditions in the presence of dissipation is formulated.
Abstract: The performance of electrical machines is largely dictated by the action of current and flux in the core length. The field in a cross-section obeys Poisson's equation and approximate solutions have been obtained by finite difference and element methods. The finite difference method requires a large number of nodes and is slow to converge as permeability is variable. The finite element method is more flexible being more readily fitted to iron-air boundaries and has better convergence. However, it is difficult to formulate a legitimate variational formulation for transient conditions in the presence of dissipation. Here, discrete equations are formed by applying Ampere's circuital law around each node. Careful choice of contour lines give a current distribution superior to that obtained with finite elements. Fast convergence is obtained and the method is applicable under transient conditions.
TL;DR: In this paper, a justification of a finite element scheme for plate bending problems is presented and some error estimates are derived for the finite element solutions of static and eigenvalue problems with the homogeneous Dirichlet conditions.
Abstract: A justification of a finite element scheme for plate bending problems is presented. The finite element treated here is the triangular element proposed by Stricklinet al. and Dhatt using the discrete Kirchhoff assumption. Some error estimates are derived for the finite element solutions of static and eigenvalue problems with the homogeneous Dirichlet conditions. Numerical experiments are also performed to see the validity of the theory.
TL;DR: In this article, a comparison between the finite difference method and the finite element method for solving the linear two-dimensional heat conduction equation is presented, and it is shown that the FEM method is superior to the FDM method in all areas except computer core storage.
TL;DR: In this article, an incremental form of virtual work is employed to derive the equations, from which the nodal displacements of the finite elements together with the generalized displacement of the analytic solution are calculated simultaneously.
TL;DR: In this article, an analysis of some finite element methods proposed for treating the Dirichlet problem is presented, where the approximation of solutions to elliptic boundary value problems via finite element type methods is discussed.
TL;DR: In this article, a fluid finite element compatible with existing structural finite elements with the ultimate objective of analysing solid-fluid interaction problems was developed, where the differential equations governing the pressure distribution in a viscous flow subjected to small amplitude oscillations were discretized on finite element subdivisions of the fluid region.
TL;DR: In this article, a general finite element approach to the problem of the determination of aeroelastic loads on a flexible vehicle flying in a state of quasi-static equilibrium is presented.
Abstract: Aerodynamic and structural influence coefficients are utilized to determine the load distributions, deflections, and trim parameters for a vehicle in quasi-static aeroelastic equilibrium. A matrix formulation is used to solve the various quasi-static aeroelastic problems. Nonlinearities in the aeroelastic trim equations are accounted for by an iteration of the classical closed form solution. Aerodynamic and structural idealizations are related by a surface spline transformation. Solutions are developed for symmetric, antisymmetric, and asymmetric load conditions on symmetric vehicles of general geometric shapes which may include both lifting surfaces and lifting bodies. INTRODUCTION With the advent of large order matrix solutions for the analysis of complex structures a need has arisen for a complementary approach to the external loads problem. Finite element structural analysis techniques demand that the external loads be distributed over the structure at discrete points. Therefore, shear, moment, and torque distributions along a psuedoelastic axis are no longer sufficient to define the external load distributions required by the stress analysis. A general finite element approach to the problem of the determination of aeroelastic loads on a flexible vehicle flying in a state of quasi-static equilibrium is presented here. The vector point loads available from this solution are directly applicable to matrix structural analyses. Structural and aerodynamic influence coefficients obtained from finite element idealizations of the aircraft are utilized as a basis for the method. The technique is primarily an extension of the method first suggested by ~ e d m a n ( l ) * and later generalized by odde en.(^) This work extends the efforts of the above-mentioned authors by * Numbers in parentheses designate References at end of paper.