| 占甫,关富玲.具有非线性homologous变形约束的桁架结构形态分析[J].计算力学学报,2007,24(5):648~653 |
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| 具有非线性homologous变形约束的桁架结构形态分析 |
| Shape analysis for truss structures with the nonlinear constraint of homologous deformation |
| 修订日期：2005-07-01 |
| DOI：10.7511/jslx20075126 |
| 中文关键词: 非线性homologous变形约束,广义逆矩阵,形态分析 |
| 英文关键词:nonlinear constraint conditions of homologous deformation,Moore-Penrose Generalized inverse,structural shape analysis |
| 基金项目: |
| 占甫 关富玲 |
| 浙江大学土木工程学系 浙江杭州310027 |
| 摘要点击次数: 999 |
| 全文下载次数: 8 |
| 中文摘要: |
| 研究了具有非线性homologous变形约束条件的桁架结构形态分析问题。在已有的线性homologous变形约束桁架形态分析的基础上,将结构的节点分成三类:homologous变形约束节点,形状可变节点和边界点。运用Moore-Penrose广义逆矩阵性质,将基础方程组解的存在条件表示为包含形状可变节点未知坐标的非线性方程组,为采用Newton-Raphson方法求解非线性方程组,对AA (A为任意矩阵,A 为A的Moore-Penrose广义逆矩阵)求偏导数,找到了满足保型要求的形态,给出的桁架算例说明了本文方法的有效性。 |
| 英文摘要: |
| This paper deals with the shape analysis for truss structures with the nonlinear constraint conditions of homologous deformation.The proposed structural shape analysis with the nonlinear constraint conditions of homologous deformation is presented,based on the structural shape analysis with the linear constraint conditions of homologous deformation.The nodal coordinates of structure can be divided into three groups: nodal coordinates under nonlinear constraint conditions of homologous deformation;free nodal coordinates and nodal coordinates under boundary constraint.Then the existence condition of solution for basic equation,which includes the proposed constraint conditions of nonlinear homologous deformation,is expressed as a set of nonlinear equations with variables of nodal coordinates under nonlinear constraint conditions of homologous deformation.The formulation is presented for the first order derivation of general matrix to its variables in oder to solve the nonlinear equation. After the solution of the nonlinear equations by Newton-Raphson method,the final shape is found out.The validity of the proposed method is verified by numerical examples concerned with elastic planar truss. |
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