Application of a second-order Godunov-type finite difference scheme to a nonlinear elastodynamic problem

✍ Scribed by J. L. Wegner; L. Jiang; J. B. Haddow

• Publisher: Springer
• Year: 1991
• Tongue: English
• Weight: 509 KB
• Volume: 8
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00370152

✦ Synopsis

A second-order Godunov-type finite difference scheme is applied to the governing equations of finite amplitude plane motion of a hyperelastic string. The governing equations, expressed in conservation form, are a hyperbolic system of four first-order partial differential equations. Numerical results are presented for a string subjected to a transverse impact at its midpoint, and the string is modelled by a strain energy function which is realistic for simple tension. Similarity solutions, valid for times before reflections occur, are in excellent agreement with the results from the finite difference scheme and provide a partial check on the validity of the scheme. Numerical results, which include the effects of reflections and interactions of waves, are shown graphically.