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31.
A two-dimensional linearized problem on plane buckling modes (BMs) of a rectangular plate with free edges, made of an elastic
orthotropic material, underbiaxial tension-compression is considered. With the use of double trigonometric basis functions,
displacement functions exactly satisfying all static boundary condition on plate edges are constructed. It is shown that the
exact analytic solutions found describe only the pure shear BMs, and if the normal stress in one direction is assumed equal
to zero, an analog of the solution given by the kinematic Timoshenko model can be obtained. Upon performing the limit passage
to the zero harmonic in the displacement functions of one of the directions, the solution to the problem of biaxial compression
can be obtained by equating the Poisson ratio to zero; in the case of uniaxial compression, this solution exactly agrees with
that following from the classical Bernoulli-Euler model.
__________
Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 2, pp. 149–170, March–April, 2007. 相似文献
32.
33.
1.IntroductionInrecenttenyears,thevoidformationandgrowthinhyperelasticmaterialhaveattractedmoreandmoreattentionandinterest.Theearliertestsfoundthatthenucleationofthemicro-voidwouldbepossibleduringthestretchingdeformationinmaterandrubbermaterials.However,t… 相似文献
34.
李逸豪徐典陈一鸣安东琦李锐 《应用数学和力学》2023,(9):1112-1121
Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
35.
由于要满足自由边的条件,使得本文所研究的板的分析相当困难。本文采用叠加法完满的解决了这个不易克服的困难,并使得边界条件能满足到任意精度,所取的位移解的每一项都严格满足控制微分方程。 相似文献
36.
37.
The natural vibrations of anisotropic rectangular plates of varying thickness with complex boundary conditions are studied
using the spline-collocation and discrete-orthogonalization methods. The basic principles of the approach are outlined. The
natural vibrations of orthotropic plates with parabolically varying thickness are calculated. The results (natural frequencies
and modes) obtained with different boundary conditions are analyzed
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 90–99, October 2005. 相似文献
38.
BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT-IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD 总被引:3,自引:0,他引:3
BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT-IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOADXuQilo... 相似文献
39.
热/机械载荷下功能梯度材料矩形厚板的弯曲行为 总被引:5,自引:2,他引:5
采用Reddy高阶剪切板理论,考虑材料物性参数随坐标和温度变化的特性,研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题,基于一维DQ法和Galerkin技术,给出了一对边固支,另对边任意约束时板弯曲问题的半解析解,以Si3N4/SUS304板为例考察了材料组份,温度场,面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。 相似文献
40.
Yu. K. Rubtsov 《International Applied Mechanics》2006,42(7):832-841
The paper discusses the scaled-boundary method as applied to electroelastic problems. As an example, the stress-intensity
factor is calculated for a thin rectangular piezoelectric plate with an edge crack
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 124–134, July 2006. 相似文献