变水深环境下中厚度浮板耦振问题的一个变分解

本文从Reissner 板的理论出发,提出并论证了变水深环境下中厚度浮板耦振问题的一个局部变分原理,它是建立中厚度浮板各种近似分析方法的一个有力工具,借助这个变分原理,文中还导得了一个计算中厚度浮板固有频率的一个变分式,数值算例表明本文方法具有精度高和省机时的优点。     

Subregion generalized variational principles for elastic thick plates

Tn this paper, the subregion generalized variational principle for elastic thick plates is proposed. Its main points may be stated as follows:1. Each subregion may be assigned arbitrarily as a potential region or complementary region. The subregion variational principles of potential energy, complementary energy and mixed energy represent three special forms of this principle.2. The number of independent variational variables in each sub-region may be assigned arbitrarily. Any one of the subregions may be assigned as a one-variable-region, two-variable-region or three-variable-region.3. The conjunction conditions of displacements and stresses on each interline of neighbouring subregions may be relaxed. On the basis of this principle the finite element analysis of non-conforming elements for thick plates can be formulated.Different finite element models for thick plates can be obtained by different applications of this principle. In particular,the subregion mixed variational principle for thick plates may be applied to formulating the subregion mixed finite element method for thick plates.     

无单元法求解任意边界条件下的中厚板弯曲问题

本文用无单元法进行不同边界条件下的中厚板弯曲问题的求解,提出了构造其近似位移函数的三种形式的权函数,从变分原理出发导出了Mindlin-Reissner中厚板弯曲问题的控制方程,并编制了相应的计算程序。数值算例表明,无单元法用于中厚板弯曲问题是合理可行的,其结果具有相当高的精度。     

基于混合状态变量的中厚板条形传递函数解

基于Mindlin板理论和改进的混合能量变分原理,建立了矩形区域中厚板问题的条形传递函数解法。该方法将矩形板在一个方向上离散为多个条形单元,而条形单元状态变量的解在单元的横向采用多项式插值,在单元的纵向直接解析求解。通过定义结点变量,并利用结点位移连续和力平衡条件,将多个简单子区域的解进行组装,可构造出分析复杂形状、复杂边界条件中厚板的条形传递函数解。数值算例表明,条形传递函数方法具有很高的计算精度。     

弹性力学状态变量体系下带有初应力的振动问题

通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的具有初应力的振动方程,并运用精细积分给出了两端简支的梁、组合梁和四边简支板及组合板在初应力下振动频率。本文结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解,为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。     

中厚板的耦合多项式基径向点插值无网格法

采用Mindlin平板理论,通过最小位能原理建立了各向同性中厚板的伽辽金整体弱式方程,形函数采用耦合多项式基的径向点插值法构造,可以直接施加本质边界条件. 算例表明,用耦合多项式基的径向点插值无网格法分析中厚板问题,具有效率高、精度高和易于实现等优点,可以避免薄板弯曲时的剪切自锁现象.     

具损伤压电智能层合中厚板的非线性动力稳定性分析

基于各向异性损伤理论和压电理论，采用能量法和Lagrange方程，建立了具损伤压电智能层合中厚板在参数激励下的非线性运动控制方程，应用增量谐波平衡法，求解了具损伤压电智能层合中厚板的非线性动力稳定性问题。算例中，分析了损伤参数和压电效应对压电智能层合板非线性动力稳定性的影响，揭示了力电耦合效应的内在特征，并与有关文献的结果进行了比较。     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

四边简支矩形中厚板的弯曲

本文采用Reissner中厚板理论求解了四边简支矩形中厚板的弯曲问题。文中首先对Reissner中厚板理论的控制方程进行了适当的变更,使之成为非耦联的二阶偏微分方程组,然后利用有限积分变换法求解所得新的控制方程,得到了四边简支矩形中厚板受均布载荷作用下的解析解。文中所述方法可用以求解具有其它边界条件和载荷的矩形中厚板的弯曲问题,同时还可移植应用于其它中厚板理论。     

厚板弹塑性混合状态Hamiltonian元的半解析法

采用初应力法并通过对增量形式Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理的修正，给出了厚板弹塑性分析的Ｈａｍｉｌｔｏｎ正则方程及其相应的半解析法。此法在厚板平面内采用通常的有限元离散，而沿板厚方向采用状态空间法给出半解析解答。     

扩展的Hellinger-Reissner原理及特殊层合杂交应力元

建立了一种非匀质材料新的、扩展的H ellinger-Reissner原理,发展了当一个单元域划分为不同材料特性子域、其元内应力场沿子域表面不连续、且位移场在子域表面也急剧变化时,一个非匀质有限元刚度列式便利方法.这种列式亦可用于对每层横向剪应变均独立处置的厚层板.基于此变分原理建立了新的具有一个无外力圆柱表面的层合杂交应力元,单元各层独立假定的应力场通过以自然坐标表示的非协调位移为权函数使齐次平衡方程变分满足的理性方法及严格满足给定圆柱面上无外力条件得到,位移场在元间及层间连续条件则分别通过Lagrange乘子进行了松弛.数值算例表明:这类新型元可有效地分析具有多类圆柱形槽孔的厚、中厚及薄层板自由孔边应力分布.     

薄板理论的正交关系及其变分原理

利用平面弹性与板弯曲的相似性理论，将弹性力学新正交关系中构造对偶向量的思路推广到 各向同性薄板弹性弯曲问题，由混合变量求解法直接得到对偶微分方程并推导了对应的变分 原理. 所导出的对偶微分矩阵具有主对角子矩阵为零矩阵的特点. 发现了两个独立的、对称 的正交关系，利用薄板弹性弯曲理论的积分形式证明了这种正交关系的成立. 在恰当选择对 偶向量后，弹性力学的新正交关系可以推广到各向同性薄板弹性弯曲理论.     

Vibration reduction of floating elastic plates in surface waves

Based on dynamical theories of water waves and dynamics of Mindlin thick plates,the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique.Without regard to the case of elastic connector,the calculated results obtained by the present method are in good agreement with those from the literature and the experiment.It can be shown that the present method is valid.Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method.Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems.     

GENERALIZED VARIATIONAL PRINCIPLESFOR VISCOELASTIC THIN AND THICK PLATES WITH DAMAGE

From the constitutive model with generalized force fields for a viscoelastic body with damage, the differential equations of motion for thin and thick plates with damage are derived under arbitrary boundary conditions. The convolution-type functionals for the bending of viscoelastic thin and thick plates with damage are presented, and the corresponding generalized variational principles are given. From these generalized principles, all the basic equations of the displacement and damage variables and initial and boundary conditions can be deduced. As an example, we compare the difference between the dynamical properties of plates with and without damage and consider the effect of damage on the dynamical properties of plates.     

Modified H-R mixed variational principle for magnetoelectroelastic bodies and state-vector equation

Based upon the Hellinger-Reissner (H-R) mixed variational principle for three-dimensional elastic bodies, the modified H-R mixed variational theorem for magnetoelectroelastic bodies was established. The state-vector equation of magnetoelectroelastic plates was derived from the proposed theorem by performing the variational operations. To lay a theoretical basis of the semi-analytical solution applied with the magnetoelectroelastic plates, the state-vector equation for the discrete element in plane was proposed through the use of the proposed principle. Finally, it is pointed out that the modified H-R mixed variational principle for pure elastic, single piezoelectric or single piezomagnetic bodies are the special cases of the present variational theorem.     

On some general variational principles for creep with applications to thin shells

A constitutive relation for a viscous material subject to small strains but finite rotations is postulated and associated variational theorems are formulated. These are similar to the principle of minimum of potential energy and the Hellinger-Reissner theorem of an elastic solid. The derivation of strain-displacement relations for thin shells subject to small strains but moderately large rotations are given. On this basis a mixed variational principle for thin viscous shells is developed. For the problem of creep collapse of long cylindrical shells under external pressure it is demonstrated that the mixed variational principle may be advantageous compared to other variational theorems. A comparison with the creep collapse theory of Hoff et al. is given.     

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature （DQ） approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.     

Thermomechanical Postbuckling of Imperfect Moderately Thick Plates on Nonlinear Elastic Foundations*

ABSTRACT

A postbuckling analysis is presented for a moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading, and resting on a softening nonlinear elastic foundation. The cases of (1) thermal postbuckling of initially compressed plates and (2) compressive post-buckling of initially heated plates are considered. The initial geometrical imperfections of the plates are taken into account. Formulations are based on Reissner-Mindlin plate theory, considering first-order shear deformation effects, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples include the performance of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. Typical results are presented in dimensionless graphical form.     

无单元法分析弹性地基板

弹性地基板的计算是学和工程师们十分关切的问题,本提出了分析Ｗｉｎｓｌｅｒ地基、双参数地基和半空间弹性地基板弯曲问题的无单元法,推导了无单元法的插值函数,从变分原理出发导出弹性地基板的刚度矩阵,给出计算实例,与其它的方法的结果进行比较,数值结果表明无单元法具有一系列优点。