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Research on under-constrained problem for large-scale eccentric structure lifting

DOI：

 作者 单位 E-mail 张树翠 安阳工学院 shucuijulu@126.com 齐朝晖 大连理工大学 zhaohuiq@dlut.edu.cn 徐金帅 大连理工大学 张欣刚 大连理工大学

吊装施工过程中被吊模块的水平度是作业要求的重要指标，通常需要增加配重调平。传统有限元方法需要补充约束以消除单元刚体位移，且需要重复计算平衡方程来求解调平载荷，效率不高。将模块的运动分解为随动坐标系的整体运动以及相对该坐标系的弹性变形，可将欠约束问题化为多体系统的静平衡问题。基于虚功率原理推导了吊装平顺时刻的节点力平衡方程以及相应的切线刚度矩阵，并将配重表示为基础配重与载荷系数相乘的形式。通过对节点力平衡方程求导，得到一组以载荷系数为自变量的微分方程，通过求解微分方程并结合水平度判据，可快速搜寻满足水平度要求的载荷系数。数值算例表明：该方法在解决偏心模块吊装欠约束问题方面具有明显的优势，在确定配重载荷方面具有较快的速度和合理的精度。

Levelness of the module is the key index during the lifting construction, under most conditions, counterweight is needed to meet the levelness requirement. If we use classical FEM for lifting analysis, additional constraints are always needed to eliminate the rigid body displacement, moreover, if we want to confirm the counterweight, we may need repetitive compute the balance equations, the computational efficiency is still unsatisfactory. To overcome these problems, the motion of the lifting module can be decomposed into the overall motion of the body reference and the elastic motion with respect to the body reference. Hence, the under-constrained problem can be converted to a static equilibrium problems of a multibody systems. In the following, the node force balance equations and its tangent stiffness matrix are obtained based on the virtual power principle. Then, the counterweight is expressed as the function of the basic counterweight and the load factor. The balance equations can then be converted to a set of ordinary differential equation (ODE), with efficient algorithm of the ODE, the counterweight can be easily and quickly obtained. Numerical examples shows that the proposed method can be a new approach for under-constrained problems and with reasonable accuracy and relatively rapid speed to obtain the counterweight.
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