A comprehensive mechanical response and dynamic stability analysis of elastically restrained bi-directional functionally graded porous microbeams in the thermal environment via mixed finite elements

Abstract

With the development of material science and technology, the usage area of microstructures has increased. Microbeams, which are the most common components of these, have attracted the attention of many researchers. A lot of research has been done on free vibration, buckling and dynamic stability behavior for microbeams. In this study, Mixed Finite Element Method (MFEM) is used. Here, free vibration, buckling and dynamic stability analysis are performed for the Timoshenko type elastically restrained bi-directional functionally graded porous microbeams in the thermal environment. In the calculation procedure, microscale effects are based on Modified Couple Stress Theory and Hamilton Principle is used to obtain the governing equations. A functional including field equations and boundary conditions (BCs) are obtained by using the Gateaux differential. One of the important advantages of MFEM is the use of C-0 type shape functions. Another major advantage is that shear locking is not observed with this method. In addition, the formulation allows closed-form integration through the sparse structure of element matrix. The reliability and accuracy of MFEM were demonstrated by comparing the results with the results of the Differential Quadrature Method from the literature for different BCs. In this work, the effects of Winkler and Pasternak elastic foundation parameters (K-w and K-p), AFG and FG power indexes (Px and Pz), thermal environment (Delta T) and partially or fully porosity (ss) were investigated. Finally, mechanical response due to the microscale structure of the problem can be directly obtained without additional processing. Examples related with inhomogeneities related with porosity were given as versatility as well.