A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalizati...A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.展开更多
A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circu...A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10972188)the Fundamental Research Funds for the Central Universities of China(No.2010121073)the Scientific Program of Fujian Province of China(No.2007F3096)
文摘A set of basic deformation modes for hybrid stress finite elements are directly derived from the element displacement field. Subsequently, by employing the so-called united orthogonal conditions, a new orthogonalization method is proposed. The result- ing orthogonal basic deformation modes exhibit simple and clear physical meanings. In addition, they do not involve any material parameters, and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements. Thereafter, a convenient approach for the identification of spurious zero-energy modes is presented using the positive definiteness property of a flexibility matrix. More- over, based on the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes, an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes is discussed. It is found that the orthogonality of the basic deformation modes is the sufficient and necessary condition for the suppression of spurious zero-energy modes. Numerical examples of 2D 4-node quadrilateral elements and 3D 8-node hexahedral elements are illustrated in detail to demonstrate the efficiency of the proposed orthogonal basic deformation mode method.
基金The work was supported by the National Natural Science Foundation of China (Grant No. 100Tz064) .
文摘A 3-dimensional hybrid stress element with a traction-free cylindrical surface based on amodified complementary energy principle has been derived for efficient and accurate analysis of stressconcentration around circular cutouts in thin to thick laminated composites. New expressions of sixstress components are developed by using three stress-functions in cylindrical co-ordinates, so that thehomogeneous equilibrium equations, the interlayer surface transverse-stresses and the traction-freeboundary condition on the cylindrical surface are satisfied exactly, while the interelement traction conti-nuity has been relaxed via the Lagrange multiplier method. Transverse-shear deformation effects areincorporated in each layer with displacement continuity enforced along interlayer surface. Selected ex-amples are used to demonstrate the efficiency and accuracy of the present special element.
