基于線(xiàn)性互補(bǔ)算法的疊梁接觸規(guī)律研究

摘 要:確定疊梁層間發(fā)生接觸的區(qū)間及接觸力分布規(guī)律是疊梁計(jì)算的關(guān)鍵.為克服以往解析解答得到的結(jié)論不合實(shí)際的現(xiàn)象，將疊梁接觸問(wèn)題構(gòu)造為線(xiàn)性互補(bǔ)問(wèn)題，并給出其一般求解過(guò)程.為驗(yàn)證該法的合理性，以梁與剛體接觸問(wèn)題的Timoshenko解答與胡海昌解答為例進(jìn)行對(duì)比分析.在此基礎(chǔ)上，對(duì)典型荷載作用下的疊梁接觸問(wèn)題進(jìn)行了計(jì)算，并對(duì)其影響因素進(jìn)行了深入研究.最后得到如下主要結(jié)論:剛度比、荷載作用形式以及剪切撓度對(duì)疊梁層間接觸規(guī)律影響均非常明顯;考慮剪切變形影響時(shí)，疊梁接觸力由集中力變?yōu)榉植剂?集中力作用下，疊梁接觸趨于點(diǎn)接觸，均布力作用下，疊梁接觸趨于線(xiàn)接觸;上下梁剛度相等是疊梁接觸力分布規(guī)律的一個(gè)轉(zhuǎn)折點(diǎn)，不同的上下梁剛度比會(huì)得到不同的接觸規(guī)律.

關(guān)鍵詞:疊梁;接觸規(guī)律;線(xiàn)性互補(bǔ)問(wèn)題;lemke算法

中圖分類(lèi)號(hào):TU 443 文獻(xiàn)標(biāo)識(shí)碼:A

Linear Complementarity Algorithm for Solving the Contact Problem of Laminated Beam

DENG Yuebao， ZHAO Minghua， YANG Minghui

(College of Civil Engineering，Hunan Univ，Changsha， Hunan 410082，China)

Abstract: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.

Key words:laminated beam; contact law; linear complementarity algorithm; lemke algorithm