中文摘要：

基于能量法分析弹性地基上含格构复合材料夹层梁的静力学性能,采用双参数模型描述芯层和地基的力学性能;使用竖向弹簧和扭转弹簧描述格构的力学性能。取边界函数与Chebyshev多项式的积作为上下面层的挠度试函数,既能保证试函数满足结构的几何边界条件,又能保证解的快速收敛性和数值计算的鲁棒性,计算结果与有限元分析相吻合。对影响结构挠度的上面层厚度、芯层厚度、格构宽度和格构数量进行了参数化分析,结果表明：面层厚度、格构宽度和数量是影响结构力学性能的重要参数,而芯层厚度的影响相对较小。在实际工程设计中,可通过合理选择夹层梁的面层厚度、格构宽度和数量达到既节约成本又满足力学性能要求的双重目的。

英文摘要：

A static analysis on sandwich beams with lattice on an elastic foundation was made based on energy principle. Two-parameter model was used to describe the function of core and foundation.Besides,the vertical spring and the torsional spring were used to describe the function of lattice. The product of Chebyshev polynomial and boundary function was used as deflection trial function. Because the outstanding mathematical features of Chebyshev polynomial could guarantee rapid convergence and the robustness of numerical calculation. Meanwhile,boundary function could ensure that trial function met the the geometric boundary conditions of the structure. The results were consistent with that of the finiteelement analysis,thus it indicated the correctness of the method used in this essay. Moreover,this essay made analysis on the heights of the upper surface layer,the length of the lattice as well as the quantity of the lattice from a parameter perspective. The results showed that the thickness of the layer and the number,and width of the lattices were the most important parameters while the effects of the thickness on the core were relatively small. The low cost and the satisfied mechanical properties were obtained by properly choosing the thickness of the layer and the number,and width of the lattices in the design of sandwich beams.