共查询到7条相似文献,搜索用时 0 毫秒
1.
Hybrid and multi-field variational principles for geometrically exact three-dimensional beams 总被引:2,自引:0,他引:2
This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. 相似文献
2.
David Yang Gao 《Acta Mechanica Sinica》1994,10(4):311-325
The post yield behavior of rigid-perfectly plastic solids at the collapse load is studied based on the finite deformation
theory. By using the general duality theory developed by Gao-Strang (1989), a global stability criteria is proposed and a
pair of dual extremum principles, expressed in terms of displacements, displacement rates and the Kirchhoff stresses are established
for plastic collapse analysis. It is proved that under large deformations, the existence of the plastic limit state at the
collapse load depends on the directional derivative of a so-called complementary gap function. The application to the nonlinear
plastic collapse theory yields a pair of dual bounding theorems for limit loading factor associated with any transient displacement
of the deformed body when the global extremum criteria are satisfied.
Dedicated to Professor Y.K. Cheung on the occasion of his 60th birthday 相似文献
3.
The paper is concerned with a hybrid finite element formulation for the geometrically exact dynamics of rods with applications to chaotic motion. The rod theory is developed for in-plane motions using the direct approach where the rod is treated as a one-dimensional Cosserat line. Shear deformation is included in the formulation. Within the elements, a linear distribution of the kinematical fields is combined with a constant distribution of the normal and shear forces. For time integration, the mid-point rule is employed. Various numerical examples of chaotic motion of straight and initially curved rods are presented proving the powerfulness and applicability of the finite element formulation. 相似文献
4.
饱和多孔介质中的混合有限元法和有限应变下应变局部化分析 总被引:1,自引:0,他引:1
对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元.固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值.基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式,导出了单元公式.进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法.对几何非线性分析,采用了共旋公式途径.数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能. 相似文献
5.
A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes 下载免费PDF全文
We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
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This paper presents a family of High‐order finite volume schemes applicable on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient ‘secondary’ reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock‐capturing capability of the scheme. This procedure combines the simplicity of the k‐exact reconstruction with the robustness of the WENO schemes and represents a systematic and unified way to construct High‐order accurate shock capturing schemes. To further improve the efficiency, an efficient problem‐independent shock detector is introduced. Several test cases are presented to demonstrate the accuracy and non‐oscillation property of the proposed schemes. The results show that the proposed schemes can predict the smooth solutions with uniformly High‐order accuracy and can capture the shock waves and contact discontinuities in high resolution. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献