基于高阶剪切变形理论的简支等截面层合梁弯曲与自由振动分析OA

The analytical solutions of bending deformation and natural frequencies of simply supported uniform section laminated beams were studied with high order shear deformation theory.On the premise that the shear strain of the laminated beam is continuous,the displacement function in exponential form was constructed for each section of the laminated beam,the general equation of the deflection curve and stress expressions of the laminated beam were derived by the displacement method of elastic mechanics,and the expression of deflection curve for simply supported uniform section laminated beams under uniform load was given.The formula for calculating the natural frequencies of the simply supported laminated beam is obtained by using the method of separation of variables method.The effectiveness of the proposed method was verified by a finite element simulation and relevant examples.The results show that the bending deformation and natural frequency of laminated beams calculated by the method are closer to the results of relevant literature.Ignoring the shear deformation and the moment of inertia will have a great influence on solving the bending deformation and natural frequencies of the laminated beam,and the influence will increase with the decrease of the span to height ratio.The research results provide a theoretical basis for the design and optimization of laminated beams with uniform section.