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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。
For the case of few geometrical nonlinear analysis of planar beam with hinged beam end, through the instantaneous element stiffness matrix in local coordinate system (with coordinate system) and then based on the relationship between the structural force and the local force in the local coordinate system and The relationship between the total displacement of the nodes and the incremental relationship obtained by the differential, the geometrical nonlinear element tangent stiffness matrix of the planar beam element under large displacement and small strain is obtained. The results show that the stiffness matrix in the local coordinate system can be established on the parameters of instantaneous configuration to better reflect the change of state variables. Based on the mechanical characteristics of the joint with the bending moment of 0, Considering the tangent stiffness matrix expression of the unit joints with the beam ends, the geometrical non-linear analysis of the example with the hinges verifies that the proposed expression has strong practical value.