Thermally induced large deflection analysis of shear deformable FGM shallow curved tubes using perturbation method

Abstract

In the present investigation, geometrically nonlinear response of a shallow curved tube subjected to thermal loading is analyzed. The tube is made of a functionally graded material (FGM), where properties are distributed across the tube radius. Thermomechancal properties of the constituents are assumed to be temperature dependent. The simple case of uniform temperature rise loading is considered. A higher order displacement field is considered for the tube which satisfies the conditions of zero tangential tractions on the inner and outer surfaces of the tube. With the aid of von Kármán strain‐displacement relations, linear thermoelastic constitutive law, and Hamilton's principle the governing equations of the tube are obtained. These equations are reduced to new two coupled equations for the case of axially immovable tubes. These new equations are solved using the two step perturbation technique for pinned and clamped tubes. Closed form expressions are provided to estimate the deflections in the FGM temperature dependent curved tubes under uniform thermal load. The effect of boundary conditions, temperature dependency of material properties, and geometrical properties are discussed via numerical examples.

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

“…A nonlocal strain gradient theory is adopted for the nonlinear bending analysis of FG beams without porosity 13 and with porosity. 14 HSDT and VKNST are used to investigate the NDFR of FG curved tubes 15 and porous FG flat panels. 16…”

“…A nonlocal strain gradient theory is adopted for the nonlinear bending analysis of FG beams without porosity 13 and with porosity. 14 HSDT and VKNST are used to investigate the NDFR of FG curved tubes 15 and porous FG flat panels. 16 Dynamic analysis of FGM cylinders under an impact loading is performed in Foroutan and Moradi-Dastjerdi 17 and Moradi-Dastjerdi et al 18 using a mesh-free method.…”

Thermal shock analysis of functionally graded sandwich curved beams using a new layerwise theory

“…Studies on transient thermal stresses also attracted the attention of researches. Babaei et al [12] investigated thermally induced deflection in shear deformable FGM shallow curved tube using perturbation method. Ootao and Tanigawa [13] studied transient thermoelastic problem for a functionally graded thick strip due to non-uniform heat supply.…”

An analytical approach of nonlinear buckling behavior of longitudinally compressed carbon nanotube‐reinforced (CNTR) cylindrical shells with CNTR stiffeners in thermal environment

“…The thin and thick cylindrical shells under longitudinal compression were investigated by using the perturbation method [27], energy method [28,29]. Some other remarkable studies on the behavior of cylindrical shells were also investigated [30][31][32], for FGM shallow curve tubes [30], metal foam-core cylindrical shells [31], for three-dimensional vibrations of laminated shells [32].…”