基于线性互补算法的叠梁接触规律研究

Linear Complementarity Algorithm for Solving the Contact Problem of Laminated Beam

确定叠梁层间发生接触的区间及接触力分布规律是叠梁计算的关键.为克服以往解析解答得到的结论不合实际的现象,将叠梁接触问题构造为线性互补问题,并给出其一般求解过程.为验证该法的合理性,以梁与刚体接触问题的Timoshenko解答与胡海昌解答为例进行对比分析.在此基础上,对典型荷载作用下的叠梁接触问题进行了计算,并对其影响因素进行了深入研究.最后得到如下主要结论:刚度比、荷载作用形式以及剪切挠度对叠梁层间接触规律影响均非常明显;考虑剪切变形影响时,叠梁接触力由集中力变为分布力;集中力作用下,叠梁接触趋于点接触,均布力作用下,叠梁接触趋于线接触;上下梁刚度相等是叠梁接触力分布规律的一个转折点,不同的上下梁刚度比会得到不同的接触规律.

Determining the contact area and the distributing law of contact force is the key to the calculation of the laminated beam.In this paper,the contact problem of laminated beam was constructed into a linear complementarity model so as to overcome some irrational conclusions of traditional analytical solution.Then,the general solving process of the proposed method was obtained.And its rationlity was verified by recalculating the contact problem of beam with the rigid body discussed by Timoshenko and Hu Haichang.On this basis,the contact law of laminated beam underlying typical loads was investigated and the factors influencing the law were studied.Finally,some conclusions were obtained.All the factors such as the stiffness ratio of laminated beam,load form and shear deformation affected the contact law noticeably.When taking into account the shear deformation in computing the laminated beam,the contact force was in the form of distributing force,or it was a concentrated force when considering no shear deformation.The contact law of laminated beam tended to be point contact under concentrated force and it was in line contact under distributing loads.The same degree of rigidity of the laminated beam was the turning point of contact press distribution.Different stiffness ratios of the laminated beam had different contact laws.