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2012•Procedia EngineeringOpen access

Stiffness Matrix of Nonlinear FEM Equilibrium Equation

Jian Liu, Tian Quan Yun, Yumei Li

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Abstract

Abstract For structural stability analysis, either tangent stiffness matrix or secant stiffness matrix is used depending on different situations. In this study, the general mathematic relationship between structural secant and tangent stiffness matrices is developed in detail based on Taylor series expression of the total potential energy. The result is important to the analysis of structural nonlinear stability. Moreover, it can be used not only in finite element method but also Rayleigh-Ritz method, Galerkin method, etc.

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What this paper is about

Abstract For structural stability analysis, either tangent stiffness matrix or secant stiffness matrix is used depending on different situations. In this study, the general mathematic relationship between structural secant and tangent stiffness matrices is developed in detail based on Taylor series expression of the total potential energy. The result is important to the analysis of structural nonlinear stability. Moreover, it can be used not only in finite element method but also Rayleigh-Ritz method, Galerkin method, etc.

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Available abstract

Abstract For structural stability analysis, either tangent stiffness matrix or secant stiffness matrix is used depending on different situations. In this study, the general mathematic relationship between structural secant and tangent stiffness matrices is developed in detail based on Taylor series expression of the total potential energy. The result is important to the analysis of structural nonlinear stability. Moreover, it can be used not only in finite element method but also Rayleigh-Ritz method, Galerkin method, etc.

Key concepts: Finite element method, Nonlinear system, Stiffness, Stiffness matrix, Matrix (chemical analysis), Structural engineering, Direct stiffness method, Materials science

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