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。     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

应力约束下薄板结构的拓扑优化

研究了应力约束下薄板结构的拓扑优化问题，分析了极限应力的影响，建立了拓扑优化的数学模型，讨论了若干优化过程中的技术问题，最后，进行了实例计算。     

单点子域积分与差分

通过稳定性分析、显式与隐式积分，表明了单点子域积分相对于差分法的优越性．     

传递辛矩阵群收敛于辛Lie群

通过作用量变分原理,给出了Hamilton正则方程离散积分的传递辛矩阵表示,利用Hamil-ton正则方程给出了其对应的Lie代数。说明了当时间区段长度趋近于0时,离散系统积分的传递辛矩阵群收敛于连续时间Hamilton系统微分方程分析积分得到的辛Lie群。     

柱状含铝炸药水下爆炸近场的特征线法研究

基于之前提出的一种含熵变项的特征线法，通过控制非等熵流中的能量释放来刻画铝粉燃烧的影响，结合简单Chapman-Jouguet模型和JWL-Miller状态方程，计算了柱形含铝炸药水下爆炸的近场参数。对比模拟结果与实验数据，发现这种特征线法可以较好地预测近场冲击波的传播迹线、爆轰产物的膨胀轨迹以及内部压缩波的反射过程。结果表明，这种特征线法可用于含铝炸药水下爆炸的近场计算，进一步可用于评估含铝炸药性能或计算水下能量输出。     

基于动力系统特性和群理论的一维周期结构瞬态响应的高效算法

基于凝聚技术、周期结构的动力特性和群理论,提出了一种求解一维周期结构瞬态响应的高效数值算法.高效求解线性方程是动力响应求解过程中的关键问题.基于结构的周期特性和凝聚技术,减小结构对应线性方程的规模.利用周期结构动力系统中线性方程的特性,证明了在给定时间步长内,作用在某个单胞的外力只会对临近的有限个单胞产生影响.基于这个性质,一维周期结构动力响应的求解可转换为一系列小规模子结构的响应分析.进一步地,将小规模子结构的动力响应转化为循环周期结构的响应分析,而循环周期结构对应的线性方程可基于群理论高效求解.数值算例表明,该算法计算效率高且节省存储要求.     

解析拟协调平面四边形单元

基于弹性平面问题的多项式解析解，构造出一种新的拟协调平面四边形单元──ＡＱＣＥ单元。算例表明该单元具有计算量小、精度高、便于应用的优点。     

应用分区非线性变分原理的杂交薄壳单元

本文讨论了高次杂交壳体元在材料非线性分析中的应用，为了更精确估计单元内各部分应力的不同影响，本文应用了分区非线性变分原理推导出杂交壳元在应力增量下应用初始应力法的失衡节点力，这使得高次杂交元在非线性分析中的优点得以充分的发挥，从而大大提高了计算精度。     

基于柔顺性与热变形双目标的多孔材料与结构几何多尺度优化设计

论文采用拓扑优化技术针对由具有均一微结构的多孔陶瓷材料构成的结构,从结构和材料两个方面进行优化设计,在轻量化的同时使得结构具有较高的刚度和特定区域较小的热变形.以机械载荷下的结构柔顺性和热载荷下结构特定区域的热变形为目标,以宏观密度和微观密度为两类独立的设计变量,对两个目标进行归一化处理,建立多目标优化模型.采用体积守...