变温和荷载作用下正交异性层合梁弹性力学解

Composite laminated structures, composed of multiple engineering materials, have wide-range applications in building engineering, aerospace, automobile industry and other fields, owing to the exceptional designability and mechanical performance. The thermodynamic behaviors of clamped orthotropic laminated beams were investigated in temperature variations and the exact solutions for thermal stresses and displacements were derived based on the theory of thermoelasticity. This method is applicable to laminated beams with arbitrary thickness and number of layers, under both loads and variable temperatures. Firstly, the clamped support was equivalently transformed into a simple support boundary and a pair of transverse boundary reaction forces through introduction of the unit impulse function and the Dirac function. Additionally, the state equation was formulated with the displacement and stress as state variables and the fundamental equations combined. The Fourier series was employed to simplify the state space equation. The relationships of displacements and stresses between the top and bottom layers of the laminated beam were sequentially derived based on the continuities of displacements and stresses at the interfaces of the adjacent layers. Ultimately, the displacement and stress at any point in the orthotropic laminated beam were determined by means of the stress and displacement boundary conditions at the upper and lower surfaces of the structure. Convergence and comparison analyses demonstrate the effectiveness and accuracy of the proposed method. Furthermore, the effects of the temperature and the length-to-thickness ratio on the distributions of displacements and stresses in the orthotropic laminated beams, were discussed in detail.