带铰平面梁元几何非线性有限元分析

针对梁端带铰的平面梁元几何非线性分析研究较少的情况,通过局部坐标系（随转坐标系）下的即时单元刚度矩阵,再基于结构坐标系与局部坐标系下杆端力及节点位移的总量关系及微分获得的增量关系,获得平面梁单元在大位移、小应变条件下的几何非线性单元切线刚度矩阵。研究结果表明：将局部坐标系下的刚度矩阵建立在即时构形的参数上,更能反映状态变量的变化,在此基础上根据带铰梁端弯矩为0的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式;通过对带铰的算例进行几何非线性分析,验证了所提出的表达式具有较强的实用价值。

Geometric nonlinear finite element analysis of plane beam element with hinge

Aimed at the situation of less research results about geometric nonlinear tangent stiffness matrix of plane beam element with hinge,starting from the element stiffness matrix of local coordinate system(co-rotational coordinate system),the non-linear tangent stiffness matrix of the plane beam element in large but small-strained displacement was derived based on total and increment relation of nodal forces and displacements between local coordinate system and global coordinate system,the increment relation of nodal forces and displacements was achieved by differential method.The results show that this method can reflect the change of variables.According to the mechanical characteristics of hinged beam,an explicit expression of the non-linear tangent stiffness matrix was derived to consider the effect of hinged beam.A computer program was developed to analyze the geometrical nonlinear behavior of several classic examples with hinges.The results verify the practical value of the proposed innovative element.