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利用推广后的Main和Spencer功能梯度板理论,研究了功能梯度矩形板在均布荷载作用下的柱面弯曲问题.采用该理论中的位移展开公式,并且材料参数沿板厚方向可以任意连续变化,但将材料由各向同性推广到正交各向异性,以及由不考虑板的横向荷载作用发展到受横向均布荷载作用.假设板在y方向无限长,从而得到了一个从弹性力学理论出发的正交各向异性功能梯度板在横向均布荷载作用下柱面弯曲问题的板理论.通过算例分析,讨论了边界条件和梯度变化程度对功能梯度板静力响应的影响. 相似文献
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本文应用有限积分变换法研究Winkler地基上四边自由正交各向异性矩形中厚板的弯曲问题.具体由正交各向异性矩形中厚板弯曲的基本方程组和边界条件出发,结合有限积分变换法及其对应的逆变换法推导出正交各向异性矩形中厚板弯曲问题的解析解.该解析解统一适用于计算各向同性/正交各向异性矩形薄板、中厚板和厚板的弯曲问题,并且通过具体算例验证了所得解析解的正确性. 相似文献
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将格栅夹层梁热弯曲等效为微极热弹性梁的受热变形,利用平面微极热弹性理论建立了微极梁受热变形的控制方程组,给出了温度载荷下微极梁的位移表达式.通过胞元能量等效的方法,得到了研究的格栅夹层梁等效微极热弹性梁材料参数.对比了等效微极梁模型和ANSYS有限元软件计算得到的温度载荷下悬臂格栅夹层梁受热弯曲变形的数值结果,两种方法得到的结果非常接近,证明了微极热弹性梁是一种简单有效的模拟格栅夹层梁热变形的等效模型. 相似文献
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空间弹性变形梁动力学的旋量系统理论方法 总被引:1,自引:0,他引:1
所谓空间弹性梁,即同时考虑受弯曲、拉伸和扭转等力作用而发生空间变形的梁.借助于刚体运动的旋量理论,引入了"变形旋量"这一概念,进而提出了空间弹性梁的旋量理论.在基本的运动学假设和材料力学理论基础上,分析并给出了梁的空间柔度.接着研究了空间弹性梁的动力学,用旋量理论分析了其动能和势能,从而得到了Lagrange算子.通过对边界条件和变形函数的讨论,进一步运用Rayleigh-Ritz方法计算了系统的振动频率.将空间弹性梁与纯弯曲、扭转或者拉伸等简单变形情况下的特征频率做了对比研究.最后,运用所提出的空间弹性梁理论研究了一关节轴线互相垂直的两空间柔性杆机械臂的动力学,通过动力学仿真发现了关节的刚性运动和空间柔性杆的弹性变形运动之间的耦合影响.该文的研究工作阐明了运用旋量系统理论解决具有空间弹性变形杆件的机构动力学问题的有效性. 相似文献
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本文利用弹性复变方法和积分方程理论,讨论两个不同材料正交各向异性弹性长条的焊接问题,给出一种新的算法,改进通常单一的积分变换方法,理论上,得出了应力分布封闭形式的解. 相似文献
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采用微分求积方法(DQ方法)讨论了计及高阶横向剪切的正交各向异性弹性板的非线性弯曲问题.导出了非线性控制方程的DQ形式,利用推广的DQWB技巧处理了高阶矩的边界条件.进一步推广并运用新的分析技术简化了非线性方程的计算.为说明该方法的可靠性和有效性,将考虑剪切变形及不计剪切变形的薄板的数值结果与三维弹性解析解及其它数值解进行了比较,同时研究了数值结果的收敛性,并考察了不同的节点分布对收敛速度的影响A·D2还考察了几何、材料参数及横向剪切效应对正交各向异性板非线性弯曲的影响.分析结果表明横向剪切效应对正交各向异性中厚板的影响是显著的. 相似文献
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D. Iaşan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(1):138-153
This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic
porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest
in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic
deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then,
the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional
problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous
circular cylinder with a special kind of inhomogeneity.
相似文献
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D. Ia?an 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,15(10):138-153
This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic
porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest
in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic
deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then,
the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional
problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous
circular cylinder with a special kind of inhomogeneity. 相似文献
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Nonlinear bending of strain gradient elastic thin beams is studied adopting Bernoulli–Euler principle. Simple nonlinear strain gradient elastic theory with surface energy is employed. In fact linear constitutive relations for strain gradient elastic theory with nonlinear strains are adopted. The governing beam equations with its boundary conditions are derived through a variational method. New terms are considered, already introduced for linear cases, indicating the importance of the cross-section area, in addition to moment of inertia in bending of thin beams. Those terms strongly increase the stiffness of the thin beam. The non-linear theory is applied to buckling problems of thin beams, especially in the study of the postbuckling behaviour. 相似文献
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R.S. Gevorgyan 《Journal of Applied Mathematics and Mechanics》2008,72(1):87-91
The asymptotic method of solving boundary-value problems of the theory of elasticity for anisotropic strips and plates is used to solve coupled dynamic problems of thermoelasticity for plates, on the faces of which the values of the temperature function and the values of the components of the displacement vector or the conditions of the mixed problem of the theory of elasticity are specified. Recurrence formulae are derived for determining the components of the displacement vector, the stress tensor and for the temperature field variation function of the plate. 相似文献
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新的正交关系被推广到正交各向异性三维弹性力学.将弹性力学新正交关系中构造对偶向量的思路推广到正交各向异性问题.将弹性力学求解辛体系的对偶向量重新排序后,提出了一种新的对偶向量.由混合变量求解法直接得到对偶微分方程.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.由于对偶微分矩阵的这一特点,对于正交各向异性三维弹性力学发现了2个独立的、对称的正交关系.采用分离变量法求解对偶微分方程.从正交各向异性弹性力学求解体系的积分形式出发,利用一些恒等式证明了新的正交关系.新的正交关系不但包含原有的辛正交关系,而且比原有的关系简洁.新正交关系的物理意义是对偶方程的解关于z坐标的对称性的体现.辛正交关系是一个广义关系,但辛正交关系可以在一定的条件下以狭义的强形式出现.新的研究成果将为研究正交各向异性三维弹性力学的解析解和有限元解提供新的有效工具. 相似文献
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Bending of a Composite Material Strip with Curved Structure in the Geometrically Nonlinear Statement
To date, bending problems for strips or plates made of composite materials with curved structure have been investigated only in the linear statement. However, in many cases, the necessity arises to investigate the corresponding bending problems in the geometrically nonlinear statement. Therefore, in the present paper, some bending problems for a composite strip with a periodically curved structure is investigated in such a statement using the exact nonlinear equations of elasticity theory in Lagrangian coordinates. The numerical results are obtained by employing the FEM with the use of the Newton-Raphson and the Modified Newton-Raphson algorithms. 相似文献
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S. Yu. Yeremenko 《Journal of Applied Mathematics and Mechanics》1993,57(6):1023-1033
An equilibrium boundary element method is proposed for solving boundary-value problems in the theory of elasticity, thermo-elasticity, the dynamical theory of elasticity, bar torsion calculations, and the bending of a plate. The idea is to use simultaneously the method of constructing bundles of functions which exactly satisfy the equilibrium equations, the boundary variational equations of mechanics, and the methods of discrete finite-element approximation. The variational method of constructing the resolving boundary equations ensures that the linear system is symmetric and easily coupled to the finite-element method. Since volume integrals are eliminated the dimensions of the problem are reduced by one, but, unlike the boundary element method, there is no need to know the fundamental solutions. The solution of some bar torsion and plate bending problems confirms the high numerical efficiency of the method. 相似文献
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O. O. Chkadua 《Mathematische Nachrichten》1995,172(1):49-64
The existence and uniqueness of solutions of the nonclassical boundary-contact problems (i.e., problems with a contact on some part of the boundaries) of elasticity for homogeneous anisotropic media are investigated in Besov and Bessel potential spaces using methods of potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied. 相似文献
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V. Ia. Tereshchenko 《Journal of Applied Mathematics and Mechanics》1980,44(6):751-755
Dual variational problem for use with the problem of minimization of the boundary functionals of three-dimensional theory of elasticity, is formulated using the method of orthogonal expansions at the boundary of the region constructed in /1/. Solutions of the initial and the dual problem obtained yield the estimates for the error of the approximate solutions of the boundary value problems of the theory of elasticity. 相似文献