Vol. 5, No. 5, 2010

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A nonlinear model of thermoelastic beams with voids, with applications

Ying Li and Chang-Jun Cheng

Vol. 5 (2010), No. 5, 805–820

We generalize the traditional Hamilton principle and give a complete nonlinear mathematical model of thermoelastic beams with voids based on this generalization, including the influences of the axial force, neutral layer inertia and rotation inertia. The differential quadrature method is used to discrete the nonlinear system on the spatial domain, and the Newton–Raphson method and Runge–Kutta method are adopted to solve the static and dynamical behaviors of the beam, respectively. The influences of the parameters on the nonlinear mechanical behavior of beam are studied in detail. The results show that the presence of voids enlarges beam deflection. And also one can see that the DQM has advantages of fewer workload, higher precision, better convergence, and so on.

generalized Hamilton variational principle, thermoelastic beam with voids, differential quadrature method, nonlinear mechanical behavior
Received: 20 December 2009
Revised: 11 April 2010
Accepted: 16 April 2010
Published: 3 December 2010
Ying Li
Shanghai Institute of Applied Mathematics and Mechanics
Shanghai University
Shanghai 200072
Chang-Jun Cheng
Shanghai Institute of Applied Mathematics and Mechanics
Department of Mechanics
Shanghai University
Shanghai 200072