Relations among stiffness coefficients of hexahedral 8-noded finite elements: A simple and efficient way to reduce the integration time

Computing coefficients in stiffness matrices of finite element analysis in computational mechanics is time consuming, especially in large non-linear dynamic problems involving large meshes. Thus, any improvement in computational procedures to reduce the integration CPU time is welcomed. In this work...

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Vydáno v:Finite elements in analysis and design Ročník 55; s. 1 - 6
Hlavní autoři: Cerrolaza, M., Osorio, J.C.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.08.2012
Elsevier
Témata:
Brick
Central processing units
Computation
Derivatives
Exact sciences and technology
Finite element method
Finite elements
Fundamental areas of phenomenology (including applications)
Hexahedral elements
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Reduced integration time
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Stiffness
Stiffness matrices
Stiffness matrix evaluation
Structural and continuum mechanics
Stiffness matrix evaluation
Finite elements
Hexahedral elements
Reduced integration time
Stiffness matrix
Sensitivity analysis
Numerical integration
Hexagonal shape
Modeling
Finite element method
Discretization
Linear equation
Function derivative
Non linear effect
Time integration
ISSN:0168-874X, 1872-6925
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Shrnutí:Computing coefficients in stiffness matrices of finite element analysis in computational mechanics is time consuming, especially in large non-linear dynamic problems involving large meshes. Thus, any improvement in computational procedures to reduce the integration CPU time is welcomed. In this work, we suggest a simple and efficient approach based on linear equations to describe the cross-relations among the element´s shape-functions derivatives to compute three coefficients of the nodal stiffness submatrix as a function of other coefficients previously computed. The coefficients can relate different degrees of freedom at a given node in the element. They are used to evaluate other coefficients inside the same nodal submatrix. Improvements ranging between 20% and 24% in CPU time are obtained when the approach is applied to three dimensional discretizations with eight-noded brick finite elements. ► A significant reduction of integration time is achieved. ► Relations among stiffness terms were encountered.
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ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2012.02.004