Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, ani...Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.展开更多
Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交...Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交界面上的传递条件在分布意义上满足。Mortar有限元法(mortar finite element method,MFEM)将MEM和有限元法(finite element method,FEM)相结合,在各区域中分别使用FEM网格离散,区域的交界面上通过施加Mortar条件实现区域间的自由度连续。该文阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了NO-MFEM的程序实现过程,使用NO-MFEM对2维静磁场问题和3维静电场问题进行了计算,并与FEM模型结果进行对比,验证了该文方法的有效性。将NO-MFEM应用于电磁分析,丰富了电磁场数值计算理论,为运动涡流问题和大规模问题的分析提供了新的选择。展开更多
采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合...采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。展开更多
We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition...We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.展开更多
文摘Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.
文摘Mortar元法(mortar element method,MEM)是一种新型区域分解算法,它允许将求解区域分解为多个子域,在各个区域以最适合子域特征的方式离散。在各个区域的交界面上,边界节点不要求逐点匹配,而是通过建立加权积分形式的Mortar条件使得交界面上的传递条件在分布意义上满足。Mortar有限元法(mortar finite element method,MFEM)将MEM和有限元法(finite element method,FEM)相结合,在各区域中分别使用FEM网格离散,区域的交界面上通过施加Mortar条件实现区域间的自由度连续。该文阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了NO-MFEM的程序实现过程,使用NO-MFEM对2维静磁场问题和3维静电场问题进行了计算,并与FEM模型结果进行对比,验证了该文方法的有效性。将NO-MFEM应用于电磁分析,丰富了电磁场数值计算理论,为运动涡流问题和大规模问题的分析提供了新的选择。
文摘采用Mortar有限单元法(mortar finite element method,MFEM)能够得到正定、对称的系数矩阵,而且刚度矩阵是分块对称的,这种特点适合于并行迭代求解。阐述了非重叠Mortar有限单元法(non-overlapping MFEM,NO-MFEM)的基本原理,介绍了适合于NO-MFEM并行计算的区域分解策略以及并行求解的基本流程。针对简单2维静电场问题,使用NO-MFEM进行了并行计算,并与理论值和串行计算结果进行对比,验证了所提方法的有效性。同时,对于非协调网格造成的计算误差进行了分析。NO-MFEM法的并行计算为工程应用中优化设计问题的区域分解和并行求解提供了一种新的选择。
基金Supported by National Natural Science Foundation of China(Grant No.11371362)the Fundamental Research Funds for the Central Universities(Grant No.2012QNA36)
文摘We prove several existence and uniqueness results for Lp （p 〉 1） solutions of reflected BSDEs with continuous barriers and generators satisfying a one-sided Osgood condition together with a general growth condition in y and a uniform continuity condition or a linear growth condition in z. A necessary and sufficient condition with respect to the growth of barrier is also explored to ensure the existence of a solution. And, we show that the solutions may be approximated by the penalization method and by some sequences of solutions of reflected BSDEs. These results are obtained due to the development of those existing ideas and methods together with the application of new ideas and techniques, and they unify and improve some known works.
