融合有限元理论的DMB方法及其在复杂超大型浮体上的应用  

Finite element based discrete-module-beam method and its applications in complex VLFS

作　　者：陈永强 张显涛[1,2,3] CHEN Yongqiang;ZHANG Xiantao(State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;SJTU Yazhou Bay Institute of Deepsea Science and Technology,Sanya 572024,China;SJTU Chong Qing Research Institute,Chongqing 401120,China)

机构地区：[1]上海交通大学海洋工程全国重点实验室,上海200240 [2]上海交通大学三亚崖州湾深海科技研究院,海南三亚572024 [3]上海交通大学重庆研究院,重庆401120

出　　处：《中国舰船研究》2024年第4期193-201,共9页Chinese Journal of Ship Research

基　　金：国家自然科学基金资助项目(42206227);海南省自然科学基金资助项目(520QN290);海南省科技计划三亚崖州湾科技城自然科学基金联合项目资助(2021JJLH0062);重庆市自然科学基金资助项目(CSTB2023NSCQMSX0432);上海交通大学深蓝基金项目资助(SL2022PT103)。

摘　　要：[目的]将有限元理论融入离散模块梁单元(DMB)方法,优化集中质量刚度矩阵的求解方式,以使DMB方法更易于处理复杂超大型浮体(VLFS)问题。[方法]使用三维势流理论进行水动力分析并给出水弹性方程;引入有限元理论,将每个子模块离散为若干微小梁单元以求解刚度阵,并基于子结构法和矩阵理论推导集中质量刚度矩阵;处理复杂边界条件时,根据边界约束模式,采用划零置一法或是直接在刚度阵中增加约束项进行处理;处理复杂连接条件时,首先更改节点编号,然后再根据连接件的特点建立连接件约束矩阵并将其融入总刚度阵中。[结果]使用DMB方法计算复杂超大型浮体的位移响应时,在边界条件选取固定端和弹簧−阻尼端、连接件选取铰接、刚性连接和弹簧阻尼连接等情况下,所得结果与直接法吻合较好。[结论]研究表明,融合有限元理论的DMB方法能够方便、快速、准确地处理复杂超大型浮体在多种复杂工况下的水弹性响应。[Objectives]This paper integrates the finite element method(FEM)with the discrete-modulebeam(DMB)method and improves the derivation of the lumped-mass stiffness matrix in order to efficiently apply the DMB method to complex and compound very large floating structures(VLFS).[Methods]First,3D potential flow theory is introduced to the DMB method to establish the hydroelastic equation.FEM theory is then introduced to discretize each macro-submodule into micro beam elements,and the lumped-mass matrix is then derived on the basis of the sub-structure approach and matrix manipulation.In dealing with complex boundary conditions,the cross-zeros-set-one approach or adding an additional constraint into the total stiffness matrix is adopted.In dealing with complex interconnections,the node numbering is first altered and then an additional constraint stiffness matrix is added to the total stiffness matrix.[Results]When the FEM+DMB method is applied to VLFS with fixed/spring-damped boundary conditions and hinged/rigid/springdamped interconnections,good agreement is shown with the results from the direct method.[Conclusions]The proposed FEM+DMB method can analyze the hydroelasticity of VLFS in complex engineering scenarios with enhanced speed and accuracy.

关 键 词：离散模块梁单元 超大型浮体 固定端 弹簧−阻尼端 弹簧阻尼连接 

分 类 号：U661.4[交通运输工程—船舶及航道工程]