• Earthquakes and Structures
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• v.22 no.5
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• pp.527-538
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• 2022

In this paper the free vibration frequencies of tri-directional functionally graded materials imperfect plate is investigated for Several plate geometries with two types of porosity (even and uneven) and different type of material configuration. The effect of several parameters such as power law index and boundary conditions have been investigated. For this purpose, an efficient computational method is developed and written under Matlab environment, based on a three-dimensional modeling and the isogeometric method is used for the discretization of the structure based on NURBS (Nonuniform rational B-spline) basis functions. The results obtained by the present method are validated by the comparison with the results given by several authors in the literature.

• Steel and Composite Structures
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• v.48 no.5
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• pp.583-597
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• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• Geomechanics and Engineering
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• v.35 no.4
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• pp.367-383
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• 2023

The present paper examines the natural frequency responses of the bi-directional (n_x-n_y, n_y-n_z and n_z-n_x) and multidirectional (n_x-n_y-n_z) functionally graded (FG) plate and curved structures with and without porosity. The even and uneven kind of porosity pattern are considered to observe the influence of porosity type and porosity index. The numerical findings have been obtained using a higher order shear deformation theory (HSDT) based isometric finite element (FE) approach generated in a MATLAB platform. According to the convergence and validation investigation, the proposed HSDT based FE model is adequate to predict free vibrational responses of multidirectional porous FG plates and curved structures. Further a parametric analysis is carried out by taking various design parameters into account. The free vibrational behavior of bidirectional (2D) and multidirectional (3D) perfect-imperfect FGM structure is examined against various power law index, support conditions, aspect, and thickness ratio, and for the curvature of curved structures. The results indicate that the maximum non-dimensional fundamental frequency (NFF) value is observed in perfect FGM plates and curved structures compared to porous FGM plates and curved structures and it is maximum for FGM plates and curved structures with uneven kind of porosity than even porosity.