In this article, THERMAL stability of beams made of functionally graded material (FGM) is considered. The derivations of equations are based on the one-dimensional theory of elasticity. The material properties vary continuously through the thickness direction. Tanigawa's model for the variation of Poisson's ratio, the modulus of shear stress, and the coefficient of THERMAL expansion is considered. The equilibrium and stability equations for the functionally graded beam under THERMAL loading are derived using the variational and force summation methods. A beam containing six different types of boundary conditions is considered and closed form solutions for the critical normalized THERMAL BUCKLING loads related to the uniform temperature rise and axial temperature difference are obtained. The results are reduced to the BUCKLING formula of beams made of pure isotropic materials….

In this paper, a semi-analytical [mite element method is presented to study the THERMAL BUCKLING behavior of moderate-thick cylindrical shells. The theory is formulated based on first shear deformation assumptions. Simplified Sanders theory and non simplified theory are employed for calculation of geometrical stiffness matrix. The results obtained from these two theories are compared which shows that the critical THERMAL BUCKLING temperature based on non-simplified theory is higher than that of the simplified Sanders theory. The material is high strength carbon and the boundary condition is clamped-clamped. The influence of fiber angle orientations is also studied.

In the aerospace industry, the usage of sandwich panels in a variety of space structures such as satellites is increasing due to their excellent features like high strength-to-weight ratio, and THERMAL insulation. These structures are subjected to a variety of THERMAL loads depending on their working conditions, which cause them to expand or contract. Since these panels are connected simultaneously by twists, BUCKLING is possible due to THERMAL loads. In this paper, the THERMAL BUCKLING analysis of a CCCC Aluminum honeycomb core sandwich panel is performed under asymmetric THERMAL loading, using ABAQUS. The face sheets are attached to the core by adhesive. THERMAL loading is assumed to be two heat fluxes of 70 watts and 20 watts, which are asymmetric, and face sheets radiate heat to their surroundings. The modeling results showed the panel does not buckle under the mentioned THERMAL loading. The critical BUCKLING stress is 750 MPa and 400 MPa where the maximum THERMAL stress is 95 MPa and 37 MPa for vertical and horizontal edges respectively, which shows a significant difference of 8 to 11 times. The temperature distribution of the various points of the panel was also obtained by calculating the maximum temperature of 84 °C at the 70-watt heat flux location and the minimum temperature of 15.65 °C in the lower-left corner. The influence of various parameters like face sheets and core cell wall thickness on BUCKLING occurrence is also discussed.

Many of the mechanical structures are employed in high temperature conditions. Any variation of temperature may cause considerable side effects such as the creation of THERMAL stress or deformation. When a structure is composed of slender members such as beams or columns, one of the main problems concerning the rise of temperature is the incidence of THERMAL BUCKLING. The continuing rise of temperature beyond the onset of THERMAL BUCKLING level, continually affects the dominant forces and deformations. To study the post BUCKLING phenomenon, following the introduction of different small deformation methods of THERMAL BUCKLING analysis, a through large deformation scheme is developed to analyze the BUCKLING of a simply supported column. For the case of large deformation analysis the validity of the results is evaluated by comparing with the results obtained by using of the small deformation theory, the linear and nonlinear simulations of ABAQUS software as well as the experimental data. The results characterize the deflection of a beam with uniformly distributed load by different solution techniques as well as the effect of temperature on the mid span deflection of a post buckled beam. Based on the obtained results, the validity of different methods is evaluated.

This artcile is concerned with THERMAL BUCKLING and THERMAL induced free vibration analyses of PCPs (perforated composite plates) with simply supported edges applying a mathematical model. The stiffness and density of PCP are defined locally using Heaviside distribution functions. The governing equations are derived based on CLPT. The present solution gives reasonable results in comparison with the few literatures. In order to inspect the structural behaviour of PCPs subjected to initial THERMAL loads, many parametric studies have been carried out. Results indicated that the presence of perforations has a significant effect on THERMAL BUCKLING and THERMAL induced fundamental frequency.

In this research, the THERMAL BUCKLING analysis of a truncated conical shell made of porous materials on elastic foundation is investigated. The equilibrium equations and the conical shell`s stability equations are obtained by using the Euler`s and the Trefftz equations. Properties of the materials used in the conical shell are considered as porous foam made of steel, which is characterized by its non-uniform distribution of porous materials along the thickness direction. Initially, the displacement field relation based on the classical model for double-curved shell is expressed in terms of the Donnell`s assumptions. Non-linear straindisplacement relations are obtained according to the von Ká rmá n assumptions by applying the Green-Lagrange strain relationship. Then, performing the Euler equations leads obtaining nonlinear equilibrium equations of cylindrical shell. The stability equations of conical shell are obtained based on neighboring equilibrium benchmark (adjacent state). In order to solve the stability equations, primarily, due to the existence of axial symmetry, we consider the cone crust displacement as a sinusoidal geometry, and then, using the generalized differential quadrature method, we solve them to obtain the critical temperature values of the BUCKLING Future. In order to validate the results, they compare with the results of other published articles. At the end of the experiment, various parameters such as dimensions, boundary conditions, cone angle, porosity parameter and elastic bed coefficients are investigated on the critical temperature of the BUCKLING.