Non-symmetrical large deformation of a shallow thin conical shell

I.IntroductionItisimportanttoresearchnon-symmetricalquestionsofshallowcollicalshellsintheoryoronapplication.Asonekindofpressurevessel'sparts,shallowconicalshellsareverycommonlyusedillellgineerillgpractice,becausethedifficultyofmanul\lctul.illgthemis'small.AlthotlghwelookupmanyChineseandtbreignperiodicalswhicharctlblctobefound,wehavenotyeth'ulldarticlesanddocumentsfornon-symmetricalandnolllinearquestionsofshitllowconictllshells.Oval'rccelltyears,ProlbssorWangXinzhiandhiscolleagueshavedonealot…     

Nonlinear deformation theory of thin shell

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Nonlinear stability of double-deck reticulated circular shallow spherical shell

Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.     

Ultimate deformation behavior of a laminated spherical shell

Summary A solution method is developed for a laminated spherical shell, subject to uniform normal tractions or constant radial displacements on the boundary. Displacements and stresses in the shell can be obtained from the solution formulas, which are as simple as those for homogeneous spherical shells. These formulas are accurate when the thicknesses of the constituent spherical layers are small in comparison with the radii of the shell, and become exact in case these thicknesses tend to zero under a fixed overall shell thickness. The solution is obtained mainly by exactly treating the product of an infinitely large number of matrices which link the displacements and stresses in different constituent spherical layers. A continuous analysis and a number of numerical results are provided to validate this development. Received 4 December 1996; accepted for publication 12 September 1997     

Controlled buckling of thin film on elastomeric substrate in large deformation

Electronic systems with large stretchability have many applications. A precisely controlled buckling strategy to increase the stretchability has been demonstrated by combining lithographically patterned surface bonding chemistry and a buckling process. The buckled geometry was assumed to have a sinusoidal form, which may result in errors to determine the strains in the film. A theoretical model is presented in this letter to study the mechanics of this type of thin film/substrate system by discarding the assumption of sinusoidal buckling geometry. It is shown that the previous model overestimates the deflection and curvature in the thin film. The results from the model agree well with finite element simulations and therefore provide design guidelines in many applications ranging from stretchable electronics to micro/nano scale surface patterning and precision metrology.     

A modified Hellinger-Reissner variational functional including only two independent variables for large displacement of thin shallow shell

I.IntroductionThemathematicalbasisofthefiniteelementmethodisthevariationalprinciple,andthedevelopmentofthefiniteelementmethodimpelsthevariationalprincipleitselftogetanewdevelopment.ThevariationalprincipIepresentedbyT.H.H.PianandP.Tongistheonethatthecontin…     

On the nonlinear stability of a truncated shallow spherical shell under a concentrated load

In this paper, the axisymmetric nonlinear stability of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is investigated by use of the modified iteration method. The analytic formulas of second approximation for determining the upper and lower critical buckling loads are obtained. This paper was read at The Third East China Symposium on Solid Mechanics, Jiuhuashan, October, 1986.     

A rate type method for large deformation problems of nonlinear elasticity

ＡＲＡＴＥＴＹＰＥＭＥＴＨＯＤＦＯＲＬＡＲＧＥＤＥＦＯＲＭＡＴＩＯＮＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＥＬＡＳＴＩＣＩＴＹＬｉａｎｇＦｅｉ（梁非）,ＺｈａｎｇＳｈａｎ－ｙｕａｎ（张善元）（ＴａｉｙｕａｎＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ...     

Unsymmetrical large deformation problem of orthotropic plates

Based upon the theory of ardsotropic plates, the unsymmetrical large deformation equations of orthotropic circular plates were derived. By using Fourier series, the partial differential equations of this problem can be transformed into sets of nonlinear differential equations . And the procedure to solve the problem using the iterative method is given .     

大变形问题分析的局部Petrov-Galerkin法

在微机电系统(MEMS)的建模和模拟研究中,大变形或大移动要充分予以考虑.用有限元法分析这类问题,由于难以避免的网格畸变,使模拟效率精度降低甚至失效,无网格方法(Meshless Method)则能在分析这类问题时显示出明显的优势,无网格局部Petrov-Galerkin(MLPG)法被誉为是一种有发展前景的真正无网格法.本文进一步发展了MLPG法,通过对任意的离散分布节点采用局部径向基函数构造插值形函数和Heaviside权函数,分析方程采用局部加权弱形式离散,建立了变量仅依赖于初始构型的完全Lagrange分析格式,最后用Newton-Raphson法迭代求解.文中分析了悬臂梁典型算例和微机电开关非线性大变形问题,通过与有限元结果的比较,表明本文提出的大变形问题无网格局部Petrov-Galerkin法具有稳定性好及收敛性快等优点.     

Nonlinear stability of spherical shallow shell under compound loads

Using a semi-analytical method,the nonlinear stability of a spherical shallow shellunder centrally distributed and concentrated loads is investigated in this paper.The longermanual calculation has been avoided when finding the approximate solution,and the P-Wmcharacteristic relation can be given analytically.     

A numerical calculation of dynamic buckling of a thin shallow spherical shell under impact

Assuming the deformation of the shell has an axial symmetrical form, we transform Marguerre's equations into difference equations, and use these equations to discuss the buckling of an elastic thin shallow spherical shell subjected to impact loads. The result shows when impact load acts on the shells, a jump of the shell takes place dependent on the values λ and the critical buckling load increases with the enlargement of the loading area.     

INSTABILITY OF TOROIDAL MEMBRANE WITH LARGE TENSILE DEFORMATION

In this paper,the problem of large axisymmetric deformation of hyperelasticmembrane is reformulated on the basis of the general theory of finite elasticity.From thefundamental equations derived here,the tensile instability of toroidal rubberlike membranewith Mooney-Rivlin’s model constitutive relation is solved by using the shooting method.The upper and lower limit loads and the response curve of the displacement to the load aregiven.     

粘弹性大变形动力响应的有限元分析

本文基于ＴｏｔａｌＬａｇｒａｎｇｉａｎ增量叠加方法，采用Ｋｉｒｃｈｈｏｆｆ应力增量和Ｇｒｅｅｎ应变增量表示的动力虚功方程和Ｋｉｒｃｈｈｏｆｆ应力－Ｇｒｅｅｎ应变的单积分型本构关系，导出粘弹性大变形的动力变分方程。依此采用Ｎｅｗｍａｒｋ法和八节点轴对称等参数元与二十节点三维等参数元编制了轴对称及三维问题的动力响应计算程序，典型例题的计算结果表明分析符合结构的物理性质。     

Nonlinear bending of shallow spherical shells on the Pasternak foundations

Based on Kármán’s nonlinear fundamental differential equations,the new approach,which combines modified iteration method with Galerkin’s one,has been put forward tosolve nonlinear bending of shallow spherical shell with concave base and clamped edges onthe Pasternak foundation under uniform loads in this paper.Mathematical expression ofload-deflection has been given;furthermore,results obtained are in good agreement withexistent ones.     

Micro-experimental study of large plastic deformation for high-purity polycrystalline aluminum

This paper aims at revealing various micro- deformation characteristics, such as crystalline slip and grain boundary slide, which are recorded under scanning electronic microscope for high-purity aluminum tensile specimen at room temperature. These experimental data provide us direct evidence for shear localization near the grain boundary network via multi- directional grain boundary slide. The nonuniform deformation induced in the grain interiors would have decisive effect on the plastic flow and failure of polycrystalline materials. Sponsored by the National Natural Science Foundation of China and the Fok Ying- Tung Education Foundation.     

无网格局部Petrov-Galerkin法求解板壳弹塑性大变形

无网格局部Petrov-Galerkin法构造的高阶光滑的形函数非常适合建立板壳结构场函数的逼近函数,是一种比较理想的研究板壳问题的方法。基于Mindlin板壳理论,采用更新拉格朗日原理和大变形条件下场量的无网格表达形式,实现了率型无网格局部Petrov-Galerkin方法对板壳弹塑性大变形的求解,算例分析表明了方法的有效性和较高的分析精度。