Finite element analysis of elasto-plastic plate bending problems using transition rectangular plate elements

In this work, the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements. The shape functions of the transition plate elements are derived based on a practical rule. The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements. The mesh convergence rates of the models including the transition elements are compared with the regular element models. To verify the developed elements, simple tests are demonstrated and various elasto-plastic problems are solved. Their results are compared with ANSYS results.

A state space solution for the bending problem of thick laminated piezoelectric open cylindrical shells

Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.

MULTIPLE RECIPROCITY METHOD WITH TWO SERIES OF SEQUENCES OF HIGH-ORDER FUNDAMENTAL SOLUTION FOR THIN PLATE BENDING

The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.

NON-SYMMETRICAL BENDING PROBLEMS OF INFINITE ANNULAR PLATES SUPPORTED ON INNER EDGE

For non-asymmetrical bending problems of elastic annular plates, the exact solutions are not fond. To bending problems of infinite annular plate with two different boundary conditions, based on the boundary integral formula,the natural boundary integral equation for the boundary value problems of the biharmonic equation and the condition of bending moment in infinity,bending solutions under non-symmetrical loads are gained by the Fourier series and convolution formulae. The formula for the solutions has nicer convergence velocity and high computational accuracy, and the calculating process is simpler. Solutions of the given examples are compared with the finite element method. The textual solutions of moments near the loads are better than the finite element method to the fact that near the concentrative loads the inners forces trend to infinite.

Research of Elastic and Elastic-Plastic Deformation on Bending Problems of Variable Stiffness Beams

A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail.First,it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material,whose elastic modulus,yield strength,and section height are functions of the axial coordinates of the beam respectively.Considering the effect of shear on the deformation of the beam,the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied.Then,the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively.The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method(DQM)when the bending stiffness varied arbitrarily.The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation,DQM,and finite element method(FEM).Simulation results verified the practicability of the proposed mechanical model,and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams.

Thermal Bending of Circular Plates for Non-Axisymmetrical Problems

Using the Green function, the boundary integral formula and natural boundary integral equation for thermal elastic problems are obtained. Then based on bending solutions to circular plates subjected to the non-axi- symmetrical load, by utilizing the Fourier series and convolution formulae, the bending solutions under non-axisymmetrical thermal conditions have been obtained. The calculating process is simple. Examples show the discussed methods are effective.

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM).

Kirchhoff板弯问题的修正Argyris元方法

主要研究了Kirchhoff板弯问题的修正Argyris元方法.分析了修正Argyris元和Argy-ris元的区别和联系,并详细比较了修正Argyris元和一些常用非协调元的自由度的个数.进一步得到了修正Argyris元方法的先验误差估计.从实用的角度出发,给出了修正Argyris元的基函数.提出了修正Argyris元方法的后验误差估计子,并证明了其有效性和可靠性.

ON MORTAR-TYPE TRUNC ELEMENT METHOD FOR PLATE BENDING PROBOEM

Wepresnet a brief introduction of applying the idea of mortar method to locally nonconforming TRUNC element for solving plate bending problem. At the interfaces, three mortar conditions, one for the value of solution in pointwise way, the other two for the normal and tangential derivatives of the solution in projection way, are provided to secure the global convergence. Afte some detailed analysis, we obtain that its error estimates in both energy norm and discrete H1 norm are optimal for u*∈H3(Ω)∩H2 0(Ω).

夹层板弯曲问题的Hoff理论的解析解

本文根据Ｈｏｆ提出的夹层板理论和胡海昌、柳春图对该理论的简化理论，提出了矩形夹层板弯曲问题的解析解的一般格式，它可以用于求解各种边界条件下矩形夹层板弯曲问题的Ｈｏｆ理论的解析解。从而，使得考虑表层抗弯刚度的矩形夹层板弯曲问题求解格式化。

重心插值Galerkin法求解梁弯曲变形问题

本文运用广义函数建立非连续载荷作用下梁弯曲变形的控制方程,采用重心有理插值函数作为试函数,利用Delta函数的积分筛选性,建立重心有理插值Galerkin法求解梁弯曲变形问题的计算公式。数值算例表明,该方法原理简单,易于程序实现,数值计算精度高。

Mathematica在材料力学弯曲问题中的应用

针对材料力学梁的弯曲问题,应用奇异函数法,将不连续的载荷写成统一的载荷函数,通过积分和代入边界条件求解剪力、弯矩、转角和挠度,并通过多个实例的计算进行验证。在详细阐述奇异函数法演算过程的基础上,应用Mathematica实现了奇异函数法算法,并绘制了弯曲问题的剪力、弯矩、转角和挠度等图形。Mathematica程序加以适当扩展,能够解决材料力学中各类问题的计算,对提高材料力学的教学能力和教学研究有着一定参考意义。

无网格局部Petrov-Galerkin法分析板弯曲的剪切自锁问题

用径向基函数构造无网格局部Petrov-Galerkin方法的形函数,插值函数具有Kronecker delta函数性质,因此可以很方便地施加本质边界条件.分析了板弯曲时剪切自锁现象产生的原因,利用无网格局部Petrov-Galerkin方法对两对边固支另对边简支中厚板的弯曲进行了分析和计算.发现无网格方法相对于有限元法等传统数值方法能更好地避免剪切锁死现象,并提出了避免剪切自锁现象发生的有效措施.

DNA纳米管的扭转刚度模型

刚度是衡量材料弹性变形难易程度的一个定量表征参数,与DNA纳米管静动力学特性及其结构生物功能密切相关.本文致力于研究DNA纳米管的扭转刚度.首先,在六角形均匀封装条件下,考虑到单个DNA杆件弯扭组合问题的静不定特点,我们利用平衡方程、变形协调方程和弹性本构方程,合理预测了DNA纳米管扭转实验中单个DNA杆件的弯扭组合变形,由此给出了DNA纳米管扭转刚度预测的解析模型.最后的结果表明,随着DNA杆数的增加,DNA纳米管的弯曲刚度显著增加,而其扭转刚度却几乎不变,合理解释了扭转实验中发现的现象.相关结论为DNA折叠结构的设计和应用提供了参考.

薄板弯曲理论中一个新的广义变分原理及其交替max,min性质

本文在薄板弯曲的经典理论中提出一个以挠度、横向剪应变、曲率、弯矩、横向剪力、边界上的未知反力为自变函数的新的变分原理,在对自变函数预加不严厉的约束后,新泛函具有一连串交替max,min的性质。

A FREE RECTANGULAR PLATE ON ELASTIC FOUNDATION

This article will discuss the bending problems of the rectangular plates with free boundaries on elastic foundations. We talk over the two cases, that is, the plate acted on its center by a concentrated force and the plate subjected to by a concentrated force equally at four corner points respectively. We select a flexural function which satisfies not only all the geometric boundary conditions on free edges wholly but also the boundary conditions of the total internal forces. We apply the variational method meanwhile and then obtain better approximate solutions.

On plane Λ-fractional linear elasticity theory

Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.

Positive Solution for a Singular Fourth-Order Differential System

In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system u(4) = φu + f (t, u, u”, φ), 0 < t < 1, -φ” = μg (t, u, u”), 0 < t < 1, u (0) = u (1) = u”(0) = u”(1) = 0, φ (0) = φ (1) = 0;where μ > 0 is a constant, and the nonlinear terms f, g may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases.

基于正交异性等效的双向加筋板结构变形简化分析方法

[目的]随着船舶不断向大型化、复杂化发展,舱段级以上的船体结构有限元模型的网格数量将急剧增加,导致碰撞、冲击、接触等大型非线性力学问题均难以求解,故提出一种基于正交异性等效的双向加筋板结构变形简化方法。[方法]首先,将现行成熟的单向加筋板平面应力简化方法推广至更复杂的双向加筋板平面弯曲问题,并引入正交方向上加筋板总惯性矩与板的惯性矩之比来反映结构的正交异性;然后,将惯性矩比值代入推广所得的加筋板等效平面弯曲本构方程,以实现材料正交异性的转化,从而在力学层面上兼顾结构的抗变形能力和中性轴移轴产生中面力的影响;最后,利用有限元计算,根据不同的位移分布对四边固支加筋板的变形模式进行分类,并将加筋板实际结果与该方法及传统方法的等效结果进行误差对比分析。[结果]对比结果表明,在船舶双向加筋板结构中,该方法最多可减少84%的网格数量,且3种变形模式下的等效误差均可控制在6%以内,远低于2种传统方法。[结论]该方法的精度较高、适用范围更广、大幅了节省计算资源,可为大型船体结构非线性力学问题的直接建模仿真计算提供解决方案。

A WAVELET METHOD FOR BENDING OF CIRCULAR PLATE WITH LARGE DEFLECTION

A wavelet method for solving strongly nonlinear boundary value problems is described, which has been demonstrated early to have a convergence rate of order 4, almost independent of the nonlinear intensity of the equations. By using such a method, we study the bending problem of a circular plate with arbitrary large deflection. As the deflection increases, the bending behavior usually exhibits a so-called plate-to-membrane transition. Capturing such a transition has ever frustrated researchers for decades. However, without introducing any addi- tional treatment, we show in this study that the proposed wavelet solutions can naturally cover the plate-membrane transition region as the plate deflection increases. In addition, the high accuracy and efficiency of the wavelet method in solving strongly nonlinear problems is numerically confirmed, and applicable scopes for the linear, the membrane and the yon Karman plate theories are identified with respect to the large deformation bending of circular plates.