Faculty of Civil and Geodetic Engineering, Ljubljana (FGGLJ)
13.
Dinamika hiperelastičnih nosilcev
Saje, Miran ; Jelenić, Gordan
A short account on dynamic behaviour of hyperelastic structural systems which may undergo finite deformations is given in this work. Uniaxial stress-strain relationships for hyperelastic material ...which follow from the Gauss and the Mooney-Rivlin expressions for unit deformation energy are derived first. A formulation is then described for the nonlinear dynamic analysis of a planar hyperelastic frame. The finite element formulation is based on the Hu-Washizu variational principle in which exact nonlinear kinematic equations of one-dimensional finite-strain beam theory are taken into account (Saje in Jelenić, 1989). Finite extensional and bending deformations are considered, while shear deformations and an initial curvature of the beam are neglected. QR algorithm for the determination of natural frequencies of the structure as the stability indicators and the Senjanović (1983) harmonic acceleration method for a step-by-step integration of dynamic equations are employed. The solution capabilities are illustrated with numerical examples where rubber or elastic frames are analysed subject to static or dynamic forces. The results show some of the advantages of the present method in solving deformation and stability of conservative or nonconservative systems
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