Stress recovery procedure for solving boundary value problems in the mechanics of a deformable solid by the finite element method

A stress recovery procedure, based on the determination of the forces at the mesh points using a stiffness matrix obtained by the finite element method for the variational Lagrange equation, is described. The vectors of the forces reduced to the mesh points are constructed for the known stiffness ma...

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Veröffentlicht in:Journal of applied mathematics and mechanics Jg. 74; H. 3; S. 341 - 348
Hauptverfasser: Rogovoi, A.A., Stolbova, O.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier Ltd 2010
Elsevier
Schlagworte:
Exact sciences and technology
Finite element method
Fundamental areas of phenomenology (including applications)
Integral equations
Mathematical analysis
Physics
Recovery
Solid mechanics
Static elasticity (thermoelasticity...)
Stiffness matrices
Stiffness matrix
Stresses
Structural and continuum mechanics
Vectors (mathematics)
Finite element method
Stiffness matrix
Boundary value problem
Normal stress
Linear elasticity
Variational calculus
Integral equation
Modeling
Lagrange equation
Fredholm equation
ISSN:0021-8928, 0021-8928
Online-Zugang:Volltext
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Zusammenfassung:A stress recovery procedure, based on the determination of the forces at the mesh points using a stiffness matrix obtained by the finite element method for the variational Lagrange equation, is described. The vectors of the forces reduced to the mesh points are constructed for the known stiffness matrices of the elements using the displacements at the mesh points found from the solution of the problem. On the other hand, these mesh point forces are determined in terms of the unknown forces distributed over the surface of an element and given shape functions. As a result, a system of Fredholm integral equations of the first kind is obtained, the solution of which gives these distributed forces. The stresses at the mesh points are determined for the values of these forces found on the surfaces of the finite element mesh (including at the mesh points) using the Cauchy relations, which relate the forces, stresses and the normal to the surface. The special features of the use of the stress recovery procedure are demonstrated for a plane problem in the linear theory of elasticity.
Bibliographie:ObjectType-Article-2
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content type line 23
ISSN:0021-8928
0021-8928
DOI:10.1016/j.jappmathmech.2010.07.010