Abstract
This chapter presents the analytical methodology for the static and dynamic problems of rectangular plates with voids in bending state subjected to vertical loads. The height of voids does not exceed half the thickness of plates. The discontinuous variation in the rigidity and mass of the plates due to the voids is expressed as a continuous function by means of the extended Dirac function. First, the general governing equations for rectangular plates with voids are proposed by using Hamilton’s principle. Second, the analytical methodologies for the static and dynamic problems are presented by means of the Galerkin method. Third, for practical use, the closed-form approximate solutions for the static and dynamic problems are proposed.
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Takabatake, H. (2019). Static and Dynamic Analyses of Rectangular Plates with Voids. In: Simplified Analytical Methods of Elastic Plates. Springer, Singapore. https://doi.org/10.1007/978-981-13-0086-8_4
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DOI: https://doi.org/10.1007/978-981-13-0086-8_4
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