Flexural Analysis of Moderately Thick Porous Microplate Under Transverse Loading Using Strain Gradient and Two Variable Theory

Abstract

Porous microplates have been greatly implemented in biomechanics equipment, such as biosensors, implantable probes, and structures. Hence, in this paper, static analysis of moderately thick, porous microplates is investigated. In order to obtain accurate results, strain gradient theory is developed, along with two variable plate theories, for precise modeling of moderately thick microplate. In addition to simple elaboration of these theories, which leads to the two decouple equilibrium equations for considering bending and shear effects, the contemplation of the length-scale parameter and thickness effect on the results is remarkable. In studying porous microplates and reinforced porous microplates, the porosity model plays a crucial role in the flexural rigidity of the plate. Therefore, various porosity models are utilized. Simply supported boundary conditions along all edges are considered for rectangular porous microplates. An analytical solution is employed for bending analysis of the porous microplate subjected to uniform distributed load. Results show that in the porous microplate, thickness, and length-scale parameter fluctuations lead to drastic change of the deflection and flexural rigidity of the microplate. Moreover, the flexural rigidity of the microplate decreases with increasing porosity. Therefore, thickness, length-scale parameter, and porosity are the main parameters in optimizing design of the microplates in different fields. Also, results indicate that the classical plate theory studying moderately thick, porous microplates rules out estimating microplate behavior.