薄板屈曲问题的回传波射矩阵法研究  

Method of Reverberation Ray Matrix for Buckling Analysis of Thin Plates

作　　者：李志炜[1] LI Zhiwei

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《山西科技》2020年第2期25-31,共7页Shanxi Science and Technology

摘　　要：基于经典板理论,将回传波射矩阵法应用于薄板的屈曲问题中,给出了用于求解临界屈曲载荷的回传波射矩阵的推导过程。通过屈曲问题的控制方程求解结构横向位移及内力的表达式,根据边界条件及跨中连续条件推导结构的传递分配矩阵,并通过对偶坐标下结构横向位移的关系推导相位矩阵,再引入转列矩阵,最终推导出回传波射矩阵。在此基础上求解线性方程组,获得结构屈曲的临界荷载。对于对边简支,另两边任意边界条件的板,回传波射矩阵法能够得到解析的结果。通过算例与已有文献的比较,验证了回传波射矩阵法的可行性和精确性。Based on the classical deformation theory,a procedure of the method of reverberation ray matrix(MRRM)is developed to perform analysis of thin plates in this paper. A computation algorithm for the reverberation ray matrix in MRRM is derived to determine buckling loading. The transverse displacement and resultant quantities are solved through the governing equation for buckling of plates. The carry-over distribution matrix can be obtained by the boundary conditions and continuity conditions of two spans. The phase matrix and permutation matrix can be obtained based on the relation between the transverse displacements under the dual coordinates. Finally,the reverberation ray matrix can be established.The buckling load can be evaluated by solving the linear set of equations. Specifically,analytical solutions are presented for buckling of the structure having two opposite simply-supported. Several numerical examples are given and compared with known solution in the literature to illustrate the validity and accurateness of MRRM for buckling analysis.

关 键 词：回传波射矩阵法 屈曲 薄板 

分 类 号：O342[理学—固体力学]