一个新的八节点非协调曲边四边形平面单元

本文在文[1]和文[2]的基础上,提出构造非协调有限元的新方法。该方法不用一般的变分原理,可适用任意变系数正定和非正定偏微分方程。利用这一方法得到一个新的八节点四边形平面应力单元。与一般有限元相比,位移和应力可提高一阶收敛精度。形成单刚矩阵时,不需要进行数值积分。单元之间的协调条件容易满足,文中给出收敛性证明。文末给出数值算例,表明利用本文的方法,应力和位移均可获得满意的数值精度。     

General solution for large deflection problems of nonhomogeneous circular plates on elastic foundation

In this paper, a new method is presented based on [1]. It can be used to solve the arbitrary nonlinear system of differential equations with variable coefficients. By this method, the general solution for large deformation of nonhomogeneous circular plates resting on an elastic foundation is derived. The convergence of the solution is proved. Finally, it is only necessary to solve a set of nonlinear algebraic equations with three unknowns. The solution obtained by the present method has large convergence range and the computation is simpler and more rapid than other numerical methods.Numerical examples given at the end of this paper indicate that satisfactory results of stress resullants and displacements can be obtained by the present method. The correctness of the theory in this paper is, confirmed.     

THE GENERAL SOLUTION FOR DYNAMIC RESPONSE OF NONHOMOGENEOUS BEAM WITH VARIABLECROSSSECTION

ＴＨＥＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＦＯＲＤＹＮＡＭＩＣＲＥＳＰＯＮＳＥＯＦＮＯＮＨＯＭＯＧＥＮＥＯＵＳＢＥＡＭＷＩＴＨＶＡＲＩＡＢＬＥＣＲＯＳＳＳＥＣＴＩＯＮＪｉＺｈｅｎ－ｙｉ（纪振义）（ＡｎｈｕｉＡｒｃｈｉｔｅｃｔｕｒａｌＩｎｄｕｓｔｒｙＣｏｌｌ...     

General analytic solution of dynamic response of beams with nonhomogeneity and variable cross-section

In this paper, a new method, the step-reduction method, is proposed to investigate the dynamic response of the Bernoulli-Euler beams with arbitrary nonhomogeneity and arbitrary variable cross-section under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform cross-section can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only     

非均匀薄板弯曲的精确元法

本文在阶梯折算法的基础上,提出构造有限元的新方法——精确元法.它不用一般变分原理,可适用于任意变系数正定和非正定偏微分方程.利用该方法,得到薄板弯曲一个非协调三角形单元,它具有6个自由度.文中给出证明,位移和内力均收敛于精确解,并有很好的精度.文末给出算例.算例表明利用本文的方法,内力和位移均可获得满意的结果.     

非均匀弹性地基圆板轴对称弯曲的一般解

本文在阶梯折算法的基础上,提出一个新的方法——精确解析法,得到了非均匀弹性地基圆板弯曲的一般解.文中导出了在任意轴对称载荷和边界条件下求解非均匀弹性地基圆板和中心带孔圆板弯曲的一般公式,并给出一致收敛于精确解的证明.文中得到的一般解可直接计算无弹性地基圆板的弯曲问题.问题最后归结为求解一个二元一次代数方程.文末给出算例,算例表明无论内力和位移均可得到满意的结果.     

非协调曲边四过形十二自由度平板变曲单元

本利用精确元法^[1]，给出一个十二自由曲边四边形板弯曲单元，该方法不需要变分原理，适用于任意正定和非正定偏微分方程。利用这个方法，单元之间的协调条件很容易满足，仅须位移和内力的单元节点上连续，即可保证所得的解收敛于精确解。利用本方法所获得的解，无论是位移还是内可力同时有二阶收敛精度。末给出数值算例，表明了本所得到的单元有非常好的精度。     

阶梯折算法的收敛条件及其一般格式

叶开沅教授创造了阶梯折算法[1].利用这个方法求解非均匀弹性力学问题,所得到的解可以用解析式表达,并具有计算量小、精度高的优点.本文通过数学上的推导,给出了阶梯折算法的收敛条件,并证明了当收敛条件满足时,所得到的解可一致收敛于精确解.文中还给出了阶梯折算法的一般格式及误差估计.由于采用矩阵形式表达,避免了以往冗长的数学表达式,使得解的形式非常简洁.文末给出算例,算例表明运用本文的理论,可以得到阶梯折算法的正确模式.     

环向和纵向加肋非均匀大变形圆柱壳的自由振动*

环向和纵向加肋非均匀圆柱壳在航空,宇航等工业广泛运用,本文使用阶梯折算法得到了环向和纵向加肋非均匀大变形圆柱壳在任意边界条件下自由振动的一般解.问题最后归结为求解一个超越代数方程,这个方程可以用一个具体的解析表达式表示出来.文中还给出了收敛性证明和算例.算例表明,利用本文的方法,可得到满意的结果.     

Free vibration of nonlinear deformation ring-and stringer-stiffened nonuniform cylindrical shell

Cylindrical shells stiffened with rings and stringers are used in many structural applications such as pipes conveying fluids or gases and acrospace. In this paper, the general solution is obtained for free vibration of nonlinear deformation ring-and stringer-stiffened cylindrical shell with arbitrary boundary condition by step reduction method^[1]. Finally, it is only necessary to solve a nonlinear algebraic equation. This equation is expressed as an analytic form. Its convergence is proved. Three numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by step reduction method. Project Supported by the Science and Technic Fund of the National Education Committee.