A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate

doi:10.1007/s10483-020-2626-6

摘要/Abstract

摘要： A procedure of the method of reverberation ray matrix (MRRM) is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners. A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading. Specifically, the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans, while the constraint condition of two remaining edges may be in any combination of free, simply-supported, and clamped boundary conditions. Furthermore, based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions, some recursive equations (REs) for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases, which promotes the computation efficiency. Several numerical examples are given, and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

关键词: multi-span, thin rectangular plate, buckling, method of reverberation ray matrix (MRRM), recursive equation (RE) Chinese Library

Abstract: A procedure of the method of reverberation ray matrix (MRRM) is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners. A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading. Specifically, the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans, while the constraint condition of two remaining edges may be in any combination of free, simply-supported, and clamped boundary conditions. Furthermore, based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions, some recursive equations (REs) for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases, which promotes the computation efficiency. Several numerical examples are given, and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis.

Key words: multi-span, thin rectangular plate, buckling, method of reverberation ray matrix (MRRM), recursive equation (RE) Chinese Library

中图分类号:

74K20
74H55

Zhiwei LI, Guohua NIE. A procedure of the method of reverberation ray matrix for the buckling analysis of a thin multi-span plate[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(7): 1055-1068.

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