Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation m
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O R I G I NA L
Truong Hoai Chinh · Tran Minh Tu Tran Quang Hung
· Do Minh Duc ·
Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function Received: 11 February 2020 / Accepted: 18 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A point interpolation meshfree method based on polynomial basic function is employed to analyze static behavior of sandwich beams with functionally graded face sheets and porous core whose mechanical properties vary continuously in the depth-direction. Transverse shear deformation is taken into account with the context of third-order beam theory which satisfies the vanishing of shear stress at the top and bottom surfaces. The equilibrium equations are derived from the principle of virtual work. Polynomial basic function is employed to construct shape functions and approximate the displacement field of computational domain. The accuracy of the computational method is confirmed by comparisons of computed results with those available in the literature. The convergence rate and effect of nodal distribution on the accuracy are examined in details. Numerical examples are performed to investigate the effects of span-to-height ratio, face sheet-core-face sheet thickness ratio, material volume fraction index, porosity coefficient, as well as different boundary conditions on transverse displacement, axial and shear stresses of the beams. Keywords Static flexural analysis · Point interpolation meshfree method · Functionally graded sandwich beams · Porous material · Third-order shear deformation beam theory
1 Introduction Functionally graded materials (FGMs) have been developing rapidly in the past two decades. Nowadays, FGMs are used widely in many engineering applications including aircraft and aerospace industry, micro- and nano-electromechanical system, thermal barrier coating etc. Many works have been carried out to study the mechanical behaviors of functionally graded structures [1–10]. Recently, porous material has been known as a new type of lightweight material with mechanical properties that change continuously along the thickness of structures like functionally graded materials. Due to possessing of excellent properties, such as high specific strength, low relative density, low weight, sound and energy absorption, reduced thermal and electrical conductivity, etc., functionally graded porous (FGP) materials have been applied in variety of industries including aerospace industry, automotive and civil engineering, biomedical industry, machine elements, etc. [11–15]. The mechanical behavior of FGP structures therefore received great attention from the scientific community, and there has been a large number of related issues published. Chen et al. investigated the free and forced vibration characteristics [16], elastic buckling and static bending [17] of FGP beams with symmetric and asymmetric porosity distributions using Timoshenko beam theory a
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