An efficient and simple refined theory for buckling analysis of functionally graded plates

In this paper, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The mechanical properties of functionally graded material are assumed to vary according to a power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates are obtained. Comparison studies are performed to verify the validity of present results. The effects of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are investigated and discussed.     

A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates

In this paper a novel numerical method based on the Moving Kriging (MK) interpolation meshfree method, integrated with a simple higher-order shear deformation plate theory for analysis of static bending, free vibration and buckling of functionally graded (FG) plates is presented. In the proposed technique, the shape functions are built by the Kriging technique which possesses the property of Kronecker delta function which makes it easy to enforce essential boundary conditions. The present formulation is based on a refined simple third-order shear deformation theory (R-STSDT), which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the plate present in the original simple third-order shear deformation theory (STSDT). In this theory, instead of assuming a specific distribution for the displacement field, the theory of elasticity is used for obtaining the kinematics of the plate deformation. We first propose the formulation, and then several numerical examples are provided to show the merits of the proposed approach.     

Buckling of laminated plates - A simple finite element based on higher-order theory

A four-noded rectangular element with seven degrees of freedom at each node is developed for buckling analysis of laminated plate structures having any number of layers with a constant thickness of individual layers. The displacement model is so chosen that it can explain adequately the parabolic distribution of transverse shear stresses and the non-linearity of in-plane displacements across the thickness. A geometrical stiffness matrix is developed using in-plane stresses. A wide range of plates from thick to thin are examined under uniaxial loading conditions. The results are compared with the existing analytical and numerical solutions. The present formulations confirm its applicability for buckling analysis of a wide range of plates.     

Post buckling response of laminated composite plate on elastic foundation with random system properties

This paper deals with second order statistics of post buckling load of shear deformable laminated composite plates resting on linear elastic foundation with random system properties. The formulation is based on higher order shear deformation plate theory in general von Karman sense, which includes foundation effect using two-parameter Pasternak model. The random system equations are derived using the principal of virtual work. A finite element method is used for spatial descretization of the laminate with a reasonable accuracy. A perturbation technique has been the first time successfully combined with direct iterative technique by neglecting the changes in nonlinear stiffness matrix due to random variation of transverse displacements during iteration. The numerical results for the second order statistics of post buckling loads are obtained. A detailed study is carried out to highlight the characteristics of the random response and its sensitivity to different foundation parameters, the plate thickness ratio, the plate aspect ratio, the support condition, the stacking sequence and the lamination angle on the post buckling response of the laminate. The results have been compared with existing results and an independent Monte Carlo simulation.     

Computing optimum design parameters of a progressive type I interval censored life test from a cost model

This work considers optimum design of a life testing experiment with progressive type I interval censoring. A cost minimization‐based optimality criterion is proposed. The proposed cost function incorporates the cost of conducting the experiment, opportunity cost, and post‐sale cost. It is shown that the proposed cost function is scale invariant for any lifetime distribution whose support does not depend on the parameters of the distribution. Weibull distribution is considered for illustration. Optimum solution is obtained by a suitable numerical method. A sensitivity analysis is undertaken to study the effect of small perturbations in lifetime model parameter values or cost coefficients. Copyright © 2017 John Wiley & Sons, Ltd.     

An analytical solution for bending of transversely isotropic thick rectangular plates with variable thickness

In this study, the bending solution of simply supported transversely isotropic thick rectangular plates with thickness variations is provided using displacement potential functions. To achieve this purpose, governing partial differential equations in terms of displacements are obtained as the quadratic and fourth order. Then, the governing equations are solved using the separation of variables method satisfying exact boundary conditions. The advantage of the purposed method is that there is no limitation on the thickness of the plate or the way the plate thickness is being varied. No simplifying assumption in the analysis process leads to the applicability and reliability of the present method to plates with any arbitrarily chosen thickness. In order to confirm the accuracy of the proposed solution, the obtained results are compared with existing published analytical works for thin variable thickness and thick constant thickness plate. Also, due to the lack of analytical research on thick plates with variable thickness, the obtained results are verified using the finite element method which shows excellent agreement. The results show that the maximum displacement of the plates with variable thickness is moved from the center toward the thinner plate edge. In addition, results exhibit the profound effects of both thickness and aspect ratio on stress distribution along the thickness of the plate. Results also show that varying thickness has not a profound impact on bending and twisting moments in transversely isotropic plates. Five different materials consist of four transversely isotropic and one isotropic, as a special case, are considered in this paper, which it is shown that the material properties have a more considerable impact on higher thickness plate.     

缓变厚度中厚板的自由振动

本文将中厚板的厚度函数按一小参数展开,并采用奇异摄动方法,把原来变系数的微分方程组化成一系列常系数微分方程组求解.文中给出了任意变厚度中厚板的自振频率计算显式表达式,由此式,我们不仅可以方便地计算出各种变厚度的自振频率值,而且也可以根据频率的要求来优化板的厚度.文中的算例表明,本文的方法具有较好的精度、方法简便、有效等其他优点,可以考虑作为分析各种变厚度板壳的振动及稳定特征问题的有效方法之一.     

Elastic stability of all edges simply supported,stepped and stiffened rectangular plate under Biaxial loading

In this paper using finite difference method the lower bound buckling load for simply supported (a) stepped and stiffened rectangular thin plate (b) linear and non-linear variation of thickness (c) uniformly distributed compressive forces in both directions (d) uniformly distributed compressive force in y direction and non-uniform distribution of compressive force in x-direction is discussed. The thin plate is divided into 900 rectangular meshes. The partial derivatives are approximated using central difference formula. Eight hundred and forty one equations are formed and using the program developed and the least eigenvalue is obtained. The buckling coefficients are calculated for different types of stepped and non prismatic plates and the results are presented in tables and graphs for ready use by designers. Buckling factors for some cases are presented in the form of three separate tables and compared with the values obtained by Xiang, Wei and Wang. The results are in close agreement.     

Thermal buckling analysis of point-supported laminated composite plates in unilateral contact

This paper deals with the thermal buckling analysis of point-supported thin laminated composite plates. The analysis is performed for rhombic and rectangular plates and two cases of bilateral and unilateral buckling. In the unilateral buckling, it is assumed that the plate is in contact with a rigid surface and lateral deflection is forced to be only in one direction. The element-free Galerkin (EFG) method is employed to discretize equilibrium equations. Point supports are modeled in the form of distinct restrained circular surfaces through developing a numerical procedure based on the Lagrange multiplier technique. The unilateral behavior of the plate is incorporated in the analysis by using the penalty method and the Heaviside contact function. The final system of nonlinear algebraic equations is solved iteratively. Two types of point support arrangements are considered and the effect of different parameters such as number of point supports, plate aspect ratio and lamination scheme on the buckling coefficient of composite plates is investigated.     

Optimum design of laminated composite plates under dynamic excitation

An integrated model for optimum weight design of symmetrically laminated composite plates subjected to dynamic excitation is presented in this work. Optimum design procedure based on flexibility and strength criteria is presented. The objective is to determine the optimum thicknesses of the laminate layers and its optimum orientations without exhibiting any failure according to Tsai-Wu failure criterion. The finite element method, based on Mindlin plate theory, is used in conjunction with an optimization method in order to determine the optimum design. Newmark algorithm, as an implicit time integration scheme, is used to discretize the time domain and calculate the transient response of the laminated composite plate. Exterior penalty method is exploited for the constrained minimization procedure. Fletcher-Powell algorithm is used for the unconstrained minimization process. To verify the capability and efficiency of the proposed model, three examples are solved. The examples deal with flexibility and stress constraints for different boundary conditions under various dynamic excitations.