AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

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.

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.

NEW SOLUTION SYSTEM FOR CIRCULAR SECTOR PLATE BENDING AND ITS APPLICATION

Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solution for the circular sector plate. The results show that the new method is 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).

AXISYMMETRIC BENDING FOR THICK LAMINATED CIRCULAR PLATE UNDER A CONCENTRATED LOAD

Based upon the fundamental equations of three dimensional elasticity, the state equation for axisymmetric bending of laminated transversely isotropic circular plate is established and the concentrated force on plate surface is expanded into Fourier_Bessel's series, therefore, an analytical solution for the problem is presented. Every fundamental equation of three dimensional elasticity can be exactly satisfied by the solution and all the independent elastic constants can be taken into account fully, furthermore, the continuity conditions between plies can also be satisfied.

THE PROBLEM OF THE NON-LINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR THIN PLATE WITH VARIABLE THICKNESS

To begin with, in this paper, the governing equations of the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with variable thickness are derived. By using 'the method of two-variable' and introducing four small parameters, the problem of the non-linear unsymmetrical bending for cylindrically orthotropic circular thin plate with linear variable thickness are studied, and the uniformly valid asymptotic solution of Nth-order for epsilon(1) and Mth-order for epsilon(2) are obtained.

Bending problems of Non-Homogeneous Cylindrical Orthotropic Circular Plate

In this paper ,the bending problem of the non-homogeneous cylindrical orthotropiccircular plate is described.A general solution for the bending of circular plate underuniformly distributed transverse load is solved.and the exact solution of such circularplate with clamped edges is obtained.

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULA RPLATE（I）

In this paper, ihe probleins of nonlinear unsymmeirucal bending for cylindricallyorthotropic circular plale are sludied by using “ the method of two-variabie”￣[1], and theuniformly valid asympiotic soluiions of Nth-order .lor ε_1 and Mth-order for ε_2 areobiained

Iterative technique for circular thin plates on Gibson elastic foundation using modified Vlasov model

In this paper, to investigate the influence of soil inhomogeneity on the bending of circular thinplates on elastic foundations, the static problem of circular thin plates on Gibson elasticfoundation is solved using an iterative method based on the modified Vlasov model. On the basisof the principle of minimum potential energy, the governing differential equations and boundaryconditions for circular thin plates on modified Vlasov foundation considering the characteristics ofGibson soil are derived. The equations for the attenuation parameter in bending problem are alsoobtained, and the issue of unknown parameters being difficult to determine is solved using theiterative method. Numerical examples are analyzed and the results are in good agreement withthose form other literatures. It proves that the method is practical and accurate. Theinhomogeneity of modified Vlasov foundations has some influence on the deformation andinternal force behavior of circular thin plates. The effects of various parameters on the bending ofcircular plates and characteristic parameters of the foundation are discussed. The modified modelfurther enriches and develops the elastic foundations. Relevant conclusions that are meaningful toengineering practice are drawn.

Modeling of normal faulting in the subducting plates of the Tonga,Japan,Izu-Bonin and Mariana Trenches:implications for near-trench plate weakening

The plate flexure and normal faulting characteristics along the Tonga, Japan, Izu-Bonin and Mariana Trenches are investigated by combining observations and modeling of elastoplastic deformation of the subducting plate. The observed average trench relief is found to be the smallest at the Japan Trench(3 km) and the largest at the Mariana Trench(4.9 km), and the average fault throw is the smallest at the Japan Trench(113 m) and the largest at the Tonga Trench(284 m). A subducting plate is modeled to bend and generate normal faults subjected to three types of tectonic loading at the trench axis: vertical loading, bending moment, and horizontal tensional force. It is inverted for the solutions of tectonic loading that best fit the observed plate flexure and normal faulting characteristics of the four trenches. The results reveal that a horizontal tensional force(HTF) for the Japan Trench is 33%, 50% and 60% smaller than those of the Mariana, Tonga and Izu-Bonin Trenches, respectively. The normal faults are modeled to penetrate to a maximum depth of 29, 23, 32 and 32 km below the sea floor for the Tonga,Japan, Izu-Bonin and Mariana Trenches, respectively, which is consistent with the depths of relocated normal faulting earthquakes in the Japan and Izu-Bonin Trenches. Moreover, it is argued that the calculated horizontal tensional force is generally positively correlated with the observed mean fault throw, while the integrated area of the reduction in the effective elastic thickness is correlated with the trench relief. These results imply that the HTF plays a key role in controlling the normal faulting pattern and that plate weakening can lead to significant increase in the trench relief.

THE ELASTIC-PLASTIC BENDING AND WRINKLING OF THIN CIRCULAR PLATES

Ⅰ. INTRODUCTIONThin circular plates, a kind of the basic structural element widely used in engineering,are of the simplest plane-stress mechanical model with double curvatures. Hence, the investigation on the fundamental mechanical properties of the thin circular plates has been attracting great attention and brought about many results. Due to the difficulties

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.

Bending,buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM

The purpose of this paper is to investigate the bending,buckling,vibration analyses of microcomposite circular-annular sandwich plate with CNT reinforced composite facesheets under hydro-thermo-magneto-mechanical loadings are presented using first order shear deformation theory(FSDT)and modified strain gradient theory(MSGT)that includes three material length scale parameters.Also,an isotropic homogeneous core is considered for microcomposite circular-annular sandwich plate.The generalized rule of mixture is employed to predict mechanical,moisture and thermal properties ofmicrocomposite sandwich plate.By using Hamilton’s principle,governing equations are solved by differential quadrature method(DQM)for a circular annular sandwich plate.The predicted results are validated by carrying out the comparison studies for the FGM plates by modified couple stress theory(MCST).The obtained results are given to indicate the influence of the material length scale parameter,core-to-facesheet thickness ratios,magnetic effect,thermal andmoisture effects on the dimensionless deflection,critical buckling load,and natural frequency of microcomposite circular sandwich plate.The results can be employed in solid-state physics,materials science,nano-electronics,and nano electro-mechanical devices such as microactuators,and microsensor.

用能量法研究双模量大挠度圆板的轴对称弯曲

双模量圆板在外载荷作用下发生轴对称弯曲变形时,会形成各向同性的拉伸区和压缩区。此种情况下,可把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量圆板的中性面位置。在此基础上,采用能量法研究了双模量大挠度圆板轴对称弯曲变形问题,将该方法计算结果与有限元计算结果进行比较,说明了该计算方法是可靠的。算例分析表明,当圆板材料拉压弹性模量相差较大时,其挠度计算不宜采用相同弹性模量经典板壳理论,而应该采用双模量板壳理论的结论。

双模量圆板弯曲变形的计算分析

双模量圆板在载荷作用下,会形成各向同性的拉伸区和压缩区,把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量圆板的中性面位置,推导出了双模量圆板的弯曲变形微分方程.对该弯曲变形微分方程积分,即可得到双模量圆板的挠度方程和内力方程.同时,还通过算例讨论分析了双模量对圆板弯曲变形的影响,得到了拉压弹性模量相差较大的圆板弯曲变形,其挠度和弯矩的计算不宜采用相同弹性模量的经典弹性理论,而应该采用双模量薄板弹性理论的结论.

功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论,导出了热/机载荷作用下,位移形式的功能梯度中厚圆/环板轴对称弯曲问题的控制方程,获得了问题的位移和内力的一般解析解.作为特例,分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板,给出了它们的解,并分析了热/机载荷作用下解的形态,讨论了横向剪切变形、材料梯度常数和边界条件,对板的轴对称弯曲行为的影响.

功能梯度与均匀圆板弯曲解的线性转换关系

基于一阶剪切理论,研究了功能梯度材料圆板与均匀圆板轴对称弯曲解之间的线性转换关系.通过理论分析和比较功能梯度材料圆板和均匀圆板在一阶剪切理论下的位移形式的轴对称弯曲控制方程,发现了功能梯度材料圆板的转角与均匀圆板的转角之间的相似转换关系.在假设材料性质沿板厚连续变化的情况下,给出了相似转换系数的解析表达式.在此基础上,进一步导出了一阶剪切理论下功能梯度圆板的挠度与经典理论下,均匀圆板的挠度之间的线性关系.从而,可将功能梯度材料圆板在一阶剪切理论下的弯曲问题求解,转化为相应均匀薄圆板在经典理论下的弯曲问题求解,以及转换系数的计算问题.这一方法为功能梯度非均匀中厚度圆板的求解提供了简捷途径,而且更便于工程应用.作为例子,采用上述方法分别求得了周边简支和夹紧条件下,梯度圆板在均布横向载荷作用下的弯曲解析解,该解答与Reddy得到的结果完全吻合.

双模量材料圆板热弯曲及热屈曲的研究

采用Galerkin原理研究了双模量材料圆板的热弯曲及热屈曲问题。建立了双模量材料圆板在热状态下的弯曲微分方程,选取Legendre多项式为试函数,采用Galerkin原理推导出了双模量材料圆板在周边为弹性支承时的热弯曲及热屈曲近似解,该近似解与有关文献计算结果的误差在2%左右,二者基本吻合,验证了本文方法的正确性。讨论分析了温度对双模量材料圆板热弯曲及热屈曲的影响,得到了随着温差增大,双模量材料圆板中点弯曲挠度也逐渐增大,屈曲临界温度随着弯曲挠度增大而减小的结论。算例研究表明:双模量材料周边为不可移简支或周边为径向不可移转动弹性约束圆板在均匀及非均匀温度场发生小挠度轴对称热屈曲是非线性变形,而周边固支圆板发生小挠度轴对称热屈曲却是线性变形;在均匀温度场中,各向同性材料周边为不可移简支或周边为径向不可移转动弹性约束圆板、周边固支圆板,发生小挠度轴对称热屈曲都是线性变形;在非均匀温度场中,各向同性材料周边为不可移简支或周边为径向不可移转动弹性约束圆板发生小挠度轴对称热屈曲是非线性变形,各向同性材料周边固支圆板发生小挠度轴对称热屈曲是线性变形。

圆柱型正交各向异性圆形薄板的非线性非对称弯曲问题（Ⅰ）

本文利用“两变量法”￣［１］研究了圆柱型正交各向异性圆形薄板在非均布横向载荷作用下的非线性非对称弯曲问题，并得到在周边为可移夹支条件下的本问题的一致有效渐近解。