横观各向同性饱和地基上中厚圆板的非轴对称振动

研究横观各向同性饱和土地基上中厚弹性圆板的非轴对称振动问题。基于横观各向同性饱和介质Biot波动方程的一般解,按混合边值问题建立了饱和地基与弹性中厚圆板非轴对称动力相互作用的对偶积分方程,并将对偶积分方程转化为易于计算的第二类Fredholm积分方程;采用数值方法求解该积分方程。数值算例结果表明,当h/a>0.05时,饱和半空间体上中厚度圆板在不同频率下的振动特性与相应频率下的刚性板的振动特性基本相同,当h/a<0.05时,板中心的位移将随h/a的减小而增大。     

Structural modeling of beams on elastic foundations with elasticity couplings

A new simplified structural model and its governing equations for beams on elastic foundations with elastic coupling are proposed. This modeling system is simple but appropriate for the initial structural design of large-scale submerged floating-beam structures moored by tension legs spaced at uniform interval along the beam. The model is actually for beam on discrete elastic supports rather than on continuous elastic foundations. Therefore, the governing equations are based on finite difference calculus and solutions for beams on discrete elastic supports with elasticity coupling are also proposed. To clarify the applicability limit of the proposed model, the equivalence between a beam on discrete elastic supports and that on continuous elastic foundation is investigated by comparisons of characteristic solutions.     

Bending Solutions for Inhomogeneous and Laminated Elastic Plates

A procedure has been developed in previous papers for constructing exact solutions of the equations of linear elasticity in a thick plate of inhomogeneous isotropic linearly elastic material in which the elastic moduli depend in any specified manner on a coordinate normal to the plane of the plate. The essential idea is that any solution of the classical thin plate or classical laminate theory equations (which are two-dimensional theories) generates, by straightforward substitutions, a solution of the three-dimensional elasticity equations for the homogeneous material. Recently this theory has been formulated in terms of functions of a complex variable. It was shown that the displacement and stress fields in the inhomogeneous material could be expressed in terms of four complex potentials that are analytic functions of the complex variable ζ = x + iy in the mid-plane of the plate. However, the analysis performed so far applies only to the case of a plate with traction-free upper and lower faces. The present paper extends these solutions to the case where the plate is bent by a pressure distribution applied to a face.     

Vibrations of a Floating Elastic Plate Due to Periodic Displacements of a Bottom Segment

The problem of the behavior of a floating elastic thin plate under periodic vibrations of a bottom segment is solved using a numerical procedure based on the Wiener-Hopf technique. The effects of the vibration frequency, the position of the vibrating bottom segment, and the fluid depth on the vibration frequencies of the fluid and plate are studied numerically.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 166–179, September–October, 2005.     

Efficient Evaluation of the Elastic Forces and the Jacobian in the Absolute Nodal Coordinate Formulation

This paper develops a new procedure for evaluating the elastic forces, the elastic energy and the jacobian of the elastic forces in the absolute nodal coordinate formulation. For this procedure, it is fundamental to use some invariant sparse matrices that are integrated in advance and have the property of transforming the evaluation of the elastic forces in a matrix multiplication process. The use of the invariant matrices avoids the integration over the volume of the element for every evaluation of the elastic forces. Great advantages can be achieved from these invariant matrices when evaluating the elastic energy and calculating the jacobian of the elastic forces as well. The exact expression of the jacobian of the differential system of equations of motion is obtained, and some advantages of using the absolute nodal coordinate formulation are pointed out. Numerical results show that there is important time saving as a result of the use of the invariant matrices.     

园柱壳中环裂纹对弹性波的散射

本文在经典弹性薄壳运动方程基础上,分析了圆柱壳中环向穿透裂纹对扭转波和膨胀波的散射,求得了反射系数及相应的动态应力强度因子。通过检查能量平衡关系验证了所用方法的正确性。     

文克勒地基上弹性薄板受有限长弹性杆冲击的动力分析

对具有初速的有限长弹性杆与文克勒地基上弹性薄板的冲击问题进行了研究，用伽辽金原理求出了冲击力及薄板位移响应的近似公式，并对计算结果作了分析讨论     

尖端具有线性粘着力作用的加层空间的界面裂纹对稳态弹性波的散射

本文研究一类粘着型界面裂纹的弹性波散射问题．文中利用积分变换和积分方程方法推导了确定这类问题的奇异积分方程组．采用围道积分技术和切比雪夫多项式展开技术，得到了待定系数的非线性代数方程组．最后本文给出裂纹尖端粘着区的大小和界面应力的数值结果．