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Derivation of Symmetric Secant Stiffness Matrices for Nonlinear Finite Element Analysis
 
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Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, I-56122 Pisa, Italy
 
 
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Paolo Sebastiano Valvo   

Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino, I-56122 Pisa, Italy
 
 
Adv. Sci. Technol. Res. J. 2022; 16(6):118-125
 
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ABSTRACT
Nonlinear finite element analysis requires the derivation of the secant elastic stiffness matrix of the discretised mechanical system. Most approaches of the literature lead to express the secant stiffness matrix as an asymmetric matrix, which then can be made symmetric by complicated numerical calculations or analytical formulae. The paper illustrates a straightforward method for the derivation of symmetric secant (and tangent) stiffness matrices for isoparametric finite elements made of hyper-elastic materials with both geometric and material nonlinearities. The method is based on the adoption of the nodal coordinates in the current configuration, instead of the nodal displacements, as the main unknowns. The method is illustrated in general for isoparametric elements with translational degrees of freedom. Specialised expressions and numerical examples are presented for truss bar elements and structures.
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