Abstract: It is very difficult to build an exact model of composite lat tice st ructures in finite element analysis because of the complexity of the st ructure of the composite lat tice , so the homogenization of the lat tice st ructure is needed to obtain an equivalent elastic constant . The basic equation of elasticity of the lat tice st ructure was deduced
according to the principle of minimum potential energy and FEM , the elastic mat rix was given based on the
equivalent of virtual st rain energy , and the equivalent of density was got based on the equivalent of the kinetic
energy. The microscopic analysis of the cell element loaded with shear and extension was conducted , so the
equivalent elastic parameters were obtained by submit ting the equivalent parameter into the deduced equation , and then the macroscopic simulation result of the equivalent model was compared with the result of the exact model . It is verified that the method has a good precision and is appropriate for such kind of analysis in the engineering field.