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Finite element limit analysis
About: Finite element limit analysis is a research topic. Over the lifetime, 5778 publications have been published within this topic receiving 175832 citations.
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25 Nov 1983TL;DR: In this paper, the authors considered the problem of finite element solutions to the scalar Helmholtz equation and showed that the solution can be found in finite elements in one dimension.
Abstract: 1. Finite elements in one dimension 2. First-order triangular elements for potential problems 3. Electromagnetics of finite elements 4. Simplex elements for the scalar Helmholtz equation 5. Differential operators in ferromagnetic materials 6. Finite elements for integral operators 7. Curvilinear, vectorial and unbounded elements 8. Time and frequency domain problems in bounded systems 9. Unbounded radiation and scattering 10. Numerical solution of finite element equations References Appendices Index.
1,238 citations
TL;DR: In this article, a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements.
Abstract: Computable a-posteriori error estimates for finite element solutions are derived in an asymptotic form for h 0 where h measures the size of the elements. The approach has similarity to the residual method but differs from it in the use of norms of negative Sobolev spaces corresponding to the given bilinear (energy) form. For clarity the presentation is restricted to one-dimensional model problems. More specifically, the source, eigenvalue, and parabolic problems are considered involving a linear, self-adjoint operator of the second order. Generalizations to more general one-dimensional problems are straightforward, and the results also extend to higher space dimensions; but this involves some additional considerations. The estimates can be used for a practical a-posteriori assessment of the accuracy of a computed finite element solution, and they provide a basis for the design of adaptive finite element solvers.
1,211 citations
TL;DR: In this article, an extended finite element method (X-FEM) for three-dimensional crack modeling is described, where a discontinuous function and two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity.
Abstract: An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.
1,141 citations
Book•
01 Jan 1976
TL;DR: In this article, the authors present a computer program for two-dimensional field problems for structural and solid mechanics, including axisymmetric elasticity and Torsion of noncircular sections.
Abstract: BASIC CONCEPTS. One-Dimensional Linear Element. A Finite Element Example. Element Matrices: Galerkin Formulation. Two-Dimensional Elements. Coordinate Systems. FIELD PROBLEMS. Two-Dimensional Field Equation. Torsion of Noncircular Sections. Derivative Boundary Conditions: Point Sources and Sinks. Irrotational Flow. Heat Transfer by Conduction and Convection. Acoustical Vibrations. Axisymmetric Field Problems. Time-Dependent Field Problems: Theoretical Considerations. Time-Dependent Field Problems: Practical Considerations. Computer Program for Two-Dimensional Field Problems. STRUCTURAL AND SOLID MECHANICS. The Axial Force Member. Element Matrices: Potential Energy Formulations. The Truss Element. A Beam Element. A Plane Frame Element. Theory of Elasticity. Two-Dimensional Elasticity. Axisymmetric Elasticity. Computer Programs for Structural and Solid Mechanics. LINEAR AND QUADRATIC ELEMENTS. Element Shape Functions. Element Matrices. Isoparametric Computer Programs. References. Appendices.
1,027 citations
1,005 citations