In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the...In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.展开更多
The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a ...The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.展开更多
A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance ...A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.展开更多
针对基于混合物理论的两相多孔介质模型 ,采用 Galerkin加权残值有限元法 ,导出求解拟静态问题的基于 u S- u F- p变量的混合有限元方程 ,由于系统方程的系数矩阵非正定 ,进而针对该方程组提出了一种迭代求解方法 ,并由分片试验得出节...针对基于混合物理论的两相多孔介质模型 ,采用 Galerkin加权残值有限元法 ,导出求解拟静态问题的基于 u S- u F- p变量的混合有限元方程 ,由于系统方程的系数矩阵非正定 ,进而针对该方程组提出了一种迭代求解方法 ,并由分片试验得出节点压力插值函数的阶须低于固体相节点位移插值函数的阶的结论。算例结果表明 ,采用基于 u S- u F- p变量的混合法计算所得的固体相和流体相速度以及固体相的有效应力与罚方法一致 ,而压力值的精度高于罚方法。展开更多
基金supported by the National Natural Science Foundation of China (Grants 11002013, 11372025)the Defense Industrial Technology Development Program (Grants A0820132001, JCKY2013601B)+1 种基金the Aeronautical Science Foundation of China (Grant 2012ZA51010)111 Project (Grant B07009) for support
文摘In this paper, based on the second-order Taylor series expansion and the difference of convex functions algo- rithm for quadratic problems with box constraints （the DCA for QB）, a new method is proposed to solve the static response problem of structures with fairly large uncertainties in interval parameters. Although current methods are effective for solving the static response problem of structures with interval parameters with small uncertainties, these methods may fail to estimate the region of the static response of uncertain structures if the uncertainties in the parameters are fairly large. To resolve this problem, first, the general expression of the static response of structures in terms of structural parameters is derived based on the second-order Taylor series expansion. Then the problem of determining the bounds of the static response of uncertain structures is transformed into a series of quadratic problems with box constraints. These quadratic problems with box constraints can be solved using the DCA approach effectively. The numerical examples are given to illustrate the accuracy and the efficiency of the proposed method when comparing with other existing methods.
基金supported by the Minisitry of Science of the Republic of Serbia (No. 144005)
文摘The paper presents the formulation and approximation of a static thermoelasticity problem that describes bilateral frictional contact between a deformable body and a rigid foundation. The friction is in the form of a nonmonotone and multivalued law. The coupling effect of the problem is neglected. Therefore, the thermic part of the problem is considered independently on the elasticity problem. For the displacement vector, we formulate one substationary problem for a non-convex, locally Lipschitz continuous functional representing the total potential energy of the body. All problems formulated in the paper are approximated with the finite element method.
文摘A geometrical theorem for the static equilibrium of a common-point-force system has been proven by means of virtual-work principle: The equilibrium point of a common-point force system has a minimal weighted distance summation to every fixed point arbitrarily given on each force line with a weighing factor proportional to corresponding force value. Especially the mechanical simulating technique for its inverse problem has been realized by means of pulley block. The conclusions for the inverse problem derived from mechanic method are in accordance with that given by the pure mathematical method, and the self-consistence of the theorem and its inverse problem has been demonstrated. Some application examples in engineering, economy and mathematics have been discussed, especially the possible application in the research of molecular structure, has also been predicted.
文摘针对基于混合物理论的两相多孔介质模型 ,采用 Galerkin加权残值有限元法 ,导出求解拟静态问题的基于 u S- u F- p变量的混合有限元方程 ,由于系统方程的系数矩阵非正定 ,进而针对该方程组提出了一种迭代求解方法 ,并由分片试验得出节点压力插值函数的阶须低于固体相节点位移插值函数的阶的结论。算例结果表明 ,采用基于 u S- u F- p变量的混合法计算所得的固体相和流体相速度以及固体相的有效应力与罚方法一致 ,而压力值的精度高于罚方法。
