大型偏心结构吊装欠约束问题研究

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。

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

Levelness of the module is the key index during the lifting operation.Under most conditions,a counterweight is needed to meet the levelness requirement.If we use the classical FEM for lifting analysis,additional constraints are always needed to eliminate the rigid body displacement,moreover,if we want to determine the counterweight,we may need repetitive enforcement of the equations of equilibrium,and thus the computational efficiency would be unsatisfactory.To overcome these problems,the motion of the lifting module can be decomposed into the rigid-body motion of the body and the elastic motion relative to the rigid body motion.Hence,the under-constrained problem can be converted to a static equilibrium problems of a multibody systems.In the following,the equations of equilibrium for model forces and the tangent stiffness matrix are obtained based on the virtual power principle.Then,the counterweight is expressed as a function of the basic counterweight and the load factor.The equations of equilibrium can then be converted to a set of ordinary differential equations(ODEs).Using an efficient algorithm for the ODEs,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 possess a reasonable accuracy and relatively rapid speed to obtain the counterweight.