An Uncoupling Strategy in the Newmark Method for Dynamic Problems
When the semidiscrete formulation of the finite element method (FEM) is employed in traditional elastodynamic problems, a system of ordinary differential equations (ODEs) is obtained. The present paper focuses on the development of a numerical strategy to decouple the resulting system by means of the implicit unconditionally stable Newmark method, allowing the parts to be solved independently, and through an iterative procedure, managing to preserve the stability and accuracy properties of the original method. It is observed that only one iteration is sufficient to achieve the same level of accuracy of the solution of the fully coupled system, rendering a very efficient algorithm. The accuracy and potentialities of the proposed decoupling strategy will be studied through the solution of two 2D structural dynamic problems that present materials with functionally graded properties.
KeywordsStructural dynamics Newmark FEM FGM
The financial support of CNPQ, FAPEMIG, UFSJ and UFJF is greatly acknowledged.
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