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Local integral equation method for viscoelastic Reissner-Mindlin plates. (English) Zbl 1143.74053

Summary: A meshless local Petrov-Galerkin method is applied to solve static and dynamic bending problems of linear viscoelastic plates described by Reissner-Mindlin theory. To this end, the correspondence principle is applied. A weak formulation for the governing equations in the Reissner-Mindlin theory with a unit test function is transformed into local integral equations on local subdomains in the mean surface of the plate. Nodal points are randomly spread on the mean surface of the plate, and each node is surrounded by a circular subdomain to which local integral equations are applied. A meshless approximation based on the moving least-squares method is employed in the numerical implementation.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74K20 Plates
74D05 Linear constitutive equations for materials with memory
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