• Advances in aircraft and spacecraft science
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• v.11 no.2
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• pp.129-152
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• 2024

The applicability of a novel incremental-iterative technique with 2D differential/integral quadrature method (DIQM) in analyzing the nonlinear behavior of Bi-directional functionally graded (BDFG) porous plate based on neutral surface is verified in the present works. A formulation of four variables high shear deformation theory is used to describe the kinematic relations with respect to neutral surface rather than mid-plane. Bi-directional material distributions are presented by power functions through both thickness and axial directions. Porosities and voids are distributed by different cosine functions. The large deformations are included within the sense of nonlinear von Kármán strains. The integro-differential equilibrium equations with associated modified boundary conditions are solved numerically and iteratively by using 2D DIQM. Model validations and parametric analysis are depicted to present the influence of neutral axis, nonlinear strains, gradation indices, elastic foundations, and modified boundary conditions on the static deflection in addition to normal and shear stresses. The proposed model is effective in analyzing the static behavior of many real applications in nuclear reactors, marine and aerospace structures with large deformations.

• Steel and Composite Structures
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• v.45 no.5
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• pp.729-747
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• 2022

The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton's principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application.