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Integral Transform Methods for Inverse Problem of Heat Conduction with Known Boundary of a thin rectangular Object and its Stresses

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Journal of Thermal Science 2012年第5期21卷 459-465页

作者： Navneet K. Lamba N. W. Khobragade Department of Mathematics MJP Educational Campus RTM Nagpur UniversityNagpur 440 033 India

The three-dimensional inverse transient thermoelastic problem for a thin rectangular object is considered within the context of the theory of generalized thermoelasticity. The upper surface of the rectangular object occupying the space D： -a〈xSa; -b〈_y〈b; 0〈z〈h; with the known boundary conditions. Laplace and Finite Marchi-Fasulo transform techniques are used to determine the unknown temperature, temperature distribution, displacement and thermal stresses on upper plane surface of a thin rectangular object. The distributions of the considered physical variables are obtained and represented graphically.

关键词： thin rectangular plate three dimensional inverse transient thermoelastic problem Marchi- Fasulo transform and Laplace transform.

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

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Applied Mathematics and Mechanics(English Edition) 2020年第7期41卷 1055-1068页

作者： Zhiwei LI Guohua NIE School of Aerospace Engineering and Applied Mechanics Tongji UniversityShanghai 200092China

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 ***,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 ***,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 *** 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)

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