共查询到20条相似文献，搜索用时 343 毫秒
1.
矩形截面梁在受多项式分布载荷作用时,用弹性力学求解的要点是正确选择应力函数。目前常见的解法是针对具体载荷和边界条件提出一个应力函数形式,若载荷形式变化,则又要重新假设应力函数,因而求解过程显得凌乱,且对于梁受三次以上分布力作用,详细的求解过程尚未见报道。本文根据弹性力学半逆解法,对矩形截面梁的主要边界上受 q(x)=q_0x~k(q_0为常数,k=0,1,2,3,4)分布力,提出一个统一的应力函数模式: 相似文献
2.
《赤峰学院学报(自然科学版)》2016,(19)
本文基于十次对称二维准晶平面弹性问题的最终控制方程,发展了在自由端受集中力作用下悬臂梁弯曲问题的逆解法.通过引入满足基本方程的试探应力函数,结合声子场和相位子场的应力边界条件,获得了声子场和相位子场位移的解析表达式.讨论了施加载荷对声子场与相位子场位移的影响. 相似文献
3.
与传统的半逆解法不一样,采用弹性力学平面直角坐标系辛体系,运用分离变量法,求出矩形梁非齐次边界条件的解.辛解法能够有效处理各种边界条件,特别是矩形梁受线性分布荷载时,显示该方法的有效性. 相似文献
4.
《赤峰学院学报(自然科学版)》2016,(17)
给出半平面中解析函数的复合边值逆问题的提法,并给出了其解法,即利用消元法,将其转化为半平面中的复合边值问题进行求解,得到半平面中复合边值逆问题的解中的未知解析函数.把所求得的解析函数代入此边值逆问题的边值条件,利用实轴上的Plemelj公式等复变函数论中的运算方法和技巧,求出此边值逆问题的解中的未知边界函数.从而,得到了该边值逆问题的全部解的具体积分表达式及可解条件. 相似文献
5.
黄炎 《清华大学教育研究》1981,(4)
弹性力学平面问题,可简化为σ_x、σ_y、τ_(xy)、υ、ν、ε_x、ε_y、γ_(xy)等八个基本未知函数,八个基本方程及相应的边界条件。可以采用以υ、ν为基本未知函数的位移解法,也可以采用以应力分量σ_x、σ_y、τ_(xy)为基本未知函数的应力解法,特别是应用应力函数法 相似文献
6.
现行的大部分弹性力学教科书,对于极坐标中由应力函数(r,θ)来求解应力分量的问题,往往都给出了不计体力时的计算公式,而对于考虑体力且体力为常值时,应力分量究竟应该怎样用应力函数来求解阐述甚少。本文就这一问题进行讨论,并给出计算公式,供教学参考。一、体力分量的坐标变换为了后面说明问题的需要先介绍体力分量在两种坐标系下的变换关系。设弹性体上任一点 M 在直角坐标中 x 向 相似文献
7.
根据钟万勰院士提出的理性有限元的基本思想,对弹性力学平面问题及空间应力问题的插值函数进行数学推导,利用线性无关组求出了插值函数的一般表达式。 相似文献
8.
从横观各向同性弹性体轴对称问题的基本方程出发,对各向同性下的Love位移函数进行了重新修正,采用位移解法的基本原理,利用Hankel积分变换和其反演变换以及Bessel函数理论,得到了材料特征值s1=s2=s时,圆形刚性承载板下横观各向同性地基的位移与应力分量的解析解. 相似文献
9.
王焕定、焦兆平编著的《有限单元法基础》这本教材,以能量法为纽带,通过能量法求解杆件结构、平面问题、空间问题。通过建立单元的位移模式,得到单元的应变与应力;通过求单元的应变能与外力势能,从而得到单元的总势能;用最小势能原理求单元刚度矩阵与等效节点载荷。最后由单元刚度矩阵组集总纲,引入边界条件,解线性方程组,求出节点位移。再将求出的节点力代入相应单元,求得单元应力与应变。 相似文献
10.
11.
何吉欢 《上海大学学报(英文版)》1997,(1)
lintroductionIn1954,byso-calledtry-and-el.l.ormethodHull]deducedtheHu-Washizupl'inciple,whichplaysan.importantroleinthehistoryofvariation.In1964,ChienlZIsystematicallydiscussedtheLagrangemultipliermethod.Withthemethod,hesuccessfullydeducedHu-Washizuprinci… 相似文献
12.
Jihuan He Ph. D. 《上海大学学报(英文版)》1997,1(1):36-41
The paper has proved that Hellinger-Reissner and Hu-Washizu variational principles are but equivalent principles in elasticity
by following three ways: 1) Lagrange multiplier method. The paper points out that only a new independent variable can be introduced
when one constraint equation has been eliminated by one Lagrange multiplier, which must be expressed as a function of the
original variable(s) and/or the new introduced variable after identification. In using Lagrange multiplier method to deduce
Hu-Washizu principle from the minimum potential energy principle, which has only one kind of independent variable namely displacement,
by eliminating the constraint equations of stress-displacement relations, one can only obtain a principle with two kinds of
variables namely displacement and stress; 2) involutory transformation, with such method Hu-Washizu variational principle
can be deduce directly from the Hellinger-Reissner variational principle under the same variational constraints of stress-strain
relation, and vice verse; 3)semi-inverse method, by which both of the above variational principles can be deduced from the
minimum potential energy principle with the same variational constraints. So the three kinds of variational functions in Hu-Washizu
variational principle are not independent to each other, the stress-strain relationships are still its constraint conditions. 相似文献
13.
Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach 总被引：1，自引：0，他引：1
LU Chao-feng LIM C.W. XU Feng 《浙江大学学报(A卷英文版)》2007,8(11):1740-1745
Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed. 相似文献
14.
INTRODUCTION Piezoelectric bimorphs (or benders), a special type of piezoelectric device, which can produce flexural deformation significantly larger than the length or thickness deformation of the individual piezoelectric layers, have been widely used as elec- troacoustic transducers, medical devices and micro- robot due to their characteristics of easy miniaturiza- tion, high positioning accuracy, sensitive response, and large displacement (e.g., Shirley and Hampton, 1978; Ha and Kim, 2… 相似文献
15.
The symplectic approach proposed and developed by Zhong et al. in 1990s for elasticity problems is a rational analytical method, in which ample experience is not needed as in the conventional semi-inverse method. In the symplectic space, elasticity problems can be solved using the method of separation of variables along with the eigenfunction expansion technique, as in traditional Fourier analysis. The eigensolutions include those corresponding to zero and nonzero eigenvalues. The latter group can be further divided into α-and β-sets. This paper reformulates the form of β-set eigensolutions to achieve the stability of numerical calculation, which is very important to obtain accurate results within the symplectic frame. An example is finally given and numerical results are compared and discussed. 相似文献
16.
Pure bending of simply supported circular plate of transversely isotropic functionally graded material 总被引：3，自引：0，他引：3
LI Xiang-yu DING Hao-jiang CHEN Wei-qiu 《浙江大学学报(A卷英文版)》2006,7(8):1324-1328
INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu… 相似文献
17.
用无网格Galerkin法求解两点边值问题,在Galerkin方程中,形函数用移动最小二乘近似构造,边值条件由位移约束方程法引入．通过数值算例分析了参数的不同取值对解的精度的影响,验证了本文方法的有效性． 相似文献
18.
讨论无限大一维六方压电准晶材料中一类裂纹中心位于矩形顶点且成双周期分布的反平面问题,利用周期对称性、保角变化、椭圆函数及施瓦兹公式,给出该问题场势函数的封闭解,进而得到了裂纹尖端的强度因子。 相似文献
19.
A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled
beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In
first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant
torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation
is established by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium,
the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to
solve the equation. The relationship between total rotation and free warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition,
under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated
to validate the current approach and the results of the current theory are compared with those of some other available methods.
The results of comparison show that the current theory provides more accurate results. In the example of a channel-shaped
cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ. 相似文献
20.
INTRODUCTION Cracks are likely to occur on the interfaces of coated materials widely applied in engineering. It is important to detect the interface cracks by non-destructive means. Detecting the scattered waves induced by interfacial cracks by using ultrasonic technique can be considered as one of the most fea- sible methods. This paper focuses on the theoretical basis for the study of wave scattering induced by interfacial cracks. In the last two decades, there has been a large number o… 相似文献