Abstract
This paper presents a higher-order shear and normal deformation theory for the static problem of functionally graded porous thick rectangular plates. The effect of thickness stretching in the functionally graded porous plates is taken into consideration. The functionally graded porous material properties vary through the plate thickness with a specific function. The governing equations are obtained via the virtual displacement principle. The static problem is solved for a simply supported plate under a sinusoidal load. The exact expressions for displacements and stresses are obtained. The influences of the functionally graded and porosity factors on the displacements and stresses of porous plates are discussed. Some validation examples are presented to show the accuracy of the present quasi-3D theory in predicting the bending response of porous plates. The effectiveness of the present model is evaluated by numerical results that include displacements and stresses of functionally graded porous plates. The field variables of functionally graded plates are very sensitive to the variation of the porosity factor.
Highlights
IntroductionPlates, and/or shells are widely used in structural design problems
Porous material beams, plates, and/or shells are widely used in structural design problems
100 13.161000 13.019919 13.019919 14.673000 14.170342 14.311072 20.150000 20.150000 14.969000 14.969000 14.969000 14.945000 14.326085 14.572361 16.049000 16.049000 11.923000 11.923000 11.932000 11.737000 11.104869 10.528310 11.990000 11.990000 8.907700 8.907700 11.93200 8.601000 8.330706 7.290624 stress will be compared with the classical plate theory (CPT), the first-order shear deformation theory (FSDT), that uses a shear correction factor K = 5 6 and those from Carrera et al [33, 34] and Neves et al [35, 36], which account for ε3 ≠ 0 and use the Carrera unified formulation (CUF)
Summary
Plates, and/or shells are widely used in structural design problems. Magnucki et al discussed bending and buckling of a rectangular porous plate taking into account the effect of shear deformation [9]. Yang et al discussed quasi-static and dynamic bending of porous beams under step loads at their free ends [11]. Sladek et al presented the first-order Mindlin theory for the bending response of porous plates according to Biots poroelastic theory [16]. Chen et al performed the buckling and bending analyses of functionally graded porous beams using the first-order beam theory [18]. Bensaid and Guenanou [19] applied the nonlocal Timoshenko beam model to present deflection and buckling of functionally graded nanoscale beams with porosity. Akbas dealt with nonlinear static deflections of functionally graded porous beams under the thermal effect with position- and temperature-dependent material properties [20]. Several important aspects that affect displacements and stresses are discussed in details
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