Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and s...Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.展开更多
基金Project(2021ZDPY0226) supported by the Fundamental Research Funds for the Central Universities,ChinaProject(20201101009) supported by the Unveiling Bidding Project of Shanxi Province of ChinaProject(202206420003) supported by the China Scholarship Council。
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10432030 and 10372088).
文摘Two-dimensional thermoelasticity analysis of functionally graded thick beams is presented using the state space method coupled with the technique of differential quadrature. Material properties vary continuously and smoothly through the beam thickness, leading to variable coefficients in the state equation derived from the elasticity equations. Approximate laminate model is employed to translate the state equation into the one with constant coefficients in each layer. To avoid numerical instability, joint coupling matrices are introduced according to the continuity conditions at interfaces in the approximate model. The differential quadrature procedure is applied to discretizing the beam in the axial direction to make easy the treatment of arbitrary end conditions. A simply-supported beam with exponentially varying material properties is considered to validate the present method. Numerical examples are performed to investigate the influences of relative parameters.
