考虑几何非线性的杆单元应变公式

考虑几何非线性的杆单元应变公式范志良（同济大学桥梁系，上海２０００９２）有限单元法在结构几何非线性分析中应用已十分广泛。在目前的本科与研究生教学中已将一般杆、梁及板单元的几何非线性列式予以介绍￣［１］，但其中对有些问题阐述不够清晰。譬如对一般的平面杆...     

考虑几何非线性的杆单元应变公式

考虑几何非线性的杆单元应变公式范志良（同济大学桥梁系，上海２０００９２）有限单元法在结构几何非线性分析中应用已十分广泛。在目前的本科与研究生教学中已将一般杆、梁及板单元的几何非线性列式予以介绍￣［１］，但其中对有些问题阐述不够清晰。譬如对一般的平面杆...     

计算力学中的样条有限元法的进展

主要评述基于变分原理、样条函数理论与状态空间理论的样条有限元法在近２０多年来的进展以及进一步发展的趋势．首先评述了国外的早期工作──截断式样条函数在力学中的应用情况．接着评述国内工作──样条有限元、样条有限点、样条单元法等优缺点,最后还介绍了目前国内外尚未报导过的,即多变量样条有限元法和样条状态变量法在动力响应中的应用．关键词变分原理,样条函数,状态空间理论,样条有限元法     

有限体积法在二维固体力学问题中的应用

推导了矩形单元的二维固体力学有限体积法公式，与解析解及有限元解进行了比较，讨论了有限体积法在非线性问题中的应用     

基于有限条带的厚/薄板矩形通用单元

基于两广义位移梁理论，利用解析试函数来建立厚／薄梁单元的横向位移、转角位移、曲率、剪应变等位移模式，构造出厚／薄梁通用单元．应用有限条带，将厚／薄梁单元的位移模式应用于厚／薄板矩形弯曲单元，直接构造出单元的横向位移、转角、曲率、剪应变，导出了单元的刚度矩阵和结点等效力，编制了计算程序，进行了数值计算和比较，结果表明，所研究的单元不出现剪切闭锁且精度较好．     

有限弹簧法在钢筋混凝土细观断裂分析中的应用

叙述了依据计算几何学的分割理论划分多边形单元的计算前处理系统，及其有限弹簧法在钢筋混凝土构件细观断裂数值模拟中的应用。该模拟系统的主要特色为：一是利用有限弹簧法的单元形状任意性来考虑混凝土断裂模拟时单元形状的影响；二是利用其变位不连续性模拟构件从微细裂缝到断裂的全过程；三是把钢筋和混凝土分别看成具有不同性质的微小构造单元来考虑其界面性质。数值模拟钢筋混凝土构件在拉伸作用下的断裂全过程，考察钢筋的螺纹抵抗作用及其保护层的约束机理。     

偏压薄壁杆稳定计算的有限杆元法

根据能量原理,综合三次B样条函数、有限单元法和经典Vlasov薄壁杆理论的优点,提出偏压薄壁杆稳定计算的有限杆元法．推导和求解过程中,同时考虑了截面扭转、翘曲和杆中面上剪应变的影响,可适用求解常用边界条件,任意截面形状的薄壁杆特征值问题．与经典方法比较显示着该文计算方法的有效性．     

预应力混凝土箱梁横向框架效应有限元分析

以预应力混凝土箱梁桥顶板纵向开裂为工程背景，以箱梁顶板与腹板交接处两个角点的转角为基本未知量，基于箱梁纵向一维单元，利用最小势能原理推导出箱梁横向框架效应有限单元法的单元刚度矩阵，及相应的单元等效节点力，对比计算表明，该有限单元法计算精度与理论分析基本一致。实桥分析表明：现行规范计算箱梁角点弯矩相对安全，对于中点弯矩相对偏于不安全，设计过程不充分考虑混凝土箱梁横向框架效应可能导致顶板的纵向开裂。本文提出的有限单元法具有概念简单、运算速度快等优点，弥补了目前商业程序的不足，对工程设计具有一定的参考意义和推广价值。     

离散元法及其耦合算法的研究综述

介绍了离散单元法的基本理论及其研究现状,以及离散单元法与有限单元法、边界单元法、界面单元法等数值计算方法耦合的研究现状和最新进展,并讨论了离散单元法今后的发展趋势及亟待解决的问题.     

非均匀介质有限元法

提出适合非均匀介质应力分析的有限元法．文中在有限单元内部采用等参变换方法模拟材料特性的变化，算例表明该法计算效率高，计算精度好．     

PRACTICE OF SOFT ROBOTICS AND INNOVATION EDUCATION

实践教学课程可以帮助学生培养动手与团队协作能力,了解理论知识的实际应用。软体机器人是近年新兴研究领域,蕴含了丰富的力学机理。本文探讨了将其应用于力学教学的选题和组织方法,并介绍了2019年清华大学空天技术科学创新实践营软体机器人项目的实施情况。14位本科生参与项目,成功制作了5个采用不同驱动方法及运动步态的软体机器人。     

安全工程流体力学创新实践教学模式探究

流体力学是安全工程类本科专业的基础必修课。通过创新安全工程流体力学理论教学模式、融合学科专业知识及改革实践教学方法,提出了教学改革总体思路和方案,梳理了安全工程流体力学中的核心知识脉络体系;将看似孤立的基础理论三大方程穿插融合在一起,并延伸至安全工程专业中的流体力学知识点,使学生明确安全工程流体力学学什么、怎么学、如何用;丰富安全工程流体力学实践教学环节,鼓励学生自主组队开展探索性自做实验,拓宽实践教学形式及方法,引导学生开展针对性虚拟仿真模拟实验,提升学生创新能力。     

SPR误差评估在动静力数值分析中的验证与应用

有限元方法是一种便捷、强大的分析方法,常用于解决工程设计和研究中的各种复杂问题,但作为一种逼近的数值分析方法,其计算结果存在一定的误差,需要利用合理的误差评估方法评价有限元解并为进一步的改进提供依据.因此,将SPR误差评估嵌入弹塑性有限元静力数值分析中,验证在该计算中SPR误差评估的可靠性,并应用于相应的流弹塑性的动力分析中,为进一步优化网格、改进有限元计算结果提供依据.     

以《力学设计与操作》课程为例，浅谈力学创新实践型教学

面对新一轮科技革命和产业变革,培养实践水平与创新能力兼具的工程人才,必须落实到课程改革．本文提出了一种力学创新实践型教学模式,以学生为中心,成果为导向,从知识、能力、价值观三个层次的培养目标出发,通过开设《力学设计与操作》课程实现对教学设计的具体实施．经过七年的持续优化改进迭代,将“学与做”稳固结合,注重理论授课与竞赛促学的反馈优化调整,发展了优质本科生科创团队,教学成果显著,深受学生欢迎．本文是对该课程的介绍、分析与总结,希望对我国“新工科”建设背景下创新型的卓越工程人才课程改革起借鉴作用．     

On using mesh-based and mesh-free methods in problems defined by Eringen’s non-local integral model: issues and remedies

With the recent success of nonlocal theories in modeling of engineering problems involving small intrinsic length scales, such as modeling of crack propagation, this paper addresses issues pertaining to cost-ineffectiveness of Eringen’s integral model. The cost effectiveness of the computation may be considered as a twofold issue; one pertaining to the non-local model and another pertaining to the numerical tool. First of all, we shall show that during the solution of problems with Eringen’s non-local integral model, there is no need to consider the integral model for the whole computational domain. In fact, the problems may be solved by just using the integral model close to the boundaries, i.e. a boundary layer effect, or around the points with singularities. In this paper we propose a partitioning strategy to remarkably reduce the computational cost. This may be considered as a gateway for solving some types of two-scale problems, e.g. those with macro/micro and nano scales, in which the small scale effects are localized just at parts of the domain. To demonstrate the efficiency of the numerical tools, we examine the performance of the finite element method (FEM), the element free Galerkin method (EFG) and the finite point method (FPM). This paves the way for using mesh-free methods in the solution of problems with non-local integral models. Examples with smooth and non-smooth solutions are considered for examining the efficiency of the methods. It will be shown that, by considering the boundary layer effect, the FEM and FPM will be efficient enough for being used in problems defined by Eringen’s non-local integral model.

     

Study on calculation methods for acoustic radiation of axisymmetric structures in finite water depth

In this paper, a kind of FEM–WSM (Finite Element Method–Wave​ Superposition Method) is used to calculate the acoustic radiation of axisymmetric structures in finite water depth. FEM is used to solve the dry modes of axisymmetric structures, and WSM is applied along with the dry mode method to consider fluid–structure interaction effects and calculate the acoustic radiated field. This method combines the advantages of FEM and WSM. On one hand, it is suitable for complex or large axisymmetric structures on the one hand. On the other hand, it has higher computational efficiency than the FEM, and the computational domain size for the water is not limited. As long as the Green’s function is tailored for the boundary condition, the acoustic radiated field of axisymmetric structures in more complex ocean acoustic environments can be calculated by using this method. Besides, a least-square method is used to reduce the distortion resulting from computational errors of the modal estimates. The influence of the number of source and field points and the finite element mesh density on the calculation accuracy are discussed, eliciting some disciplinary conclusions. Using a spherical shell and a capsule shell as models, the results from the present approach, a semi-analytical method, and the crude FEM are compared to verify the correctness and efficiency. Based on numerical examples, the influence of the sea surface and the seafloor on the acoustic radiated field of structures in finite water depth is also analyzed.     

非线性有限元分析的非协调模式及存在的问题

利用非协调模式提高非线性有限元分析广泛采用的低阶单元的精度和性能,是国际 计算力学界研究的热点和难点.阐述了国际上在非线性有限元分析中已广泛采用的 增广假设应变法方法(the enhanced assumed strain, EAS)的基本原理,详细讨论了非协调 模式用于非线性有限元分析保证收敛、稳定的条件及增广假设应变场插值函数的构造方法. 介绍了国内学者关于几何非线性非协调模式的研究方法和研究成果: (1)从Hellinger-Reissner 广义变分原理出发,提出了几何非线性非协调模式的收敛条件,并采用非线性计算的若干简 化措施建立几何非线性非协调元的简化模型;(2)一类放松单元间协调要求的非线性广义变 分原理,对几何非线性问题可以选择事先无协调约束的非协调函数建立非协调元,收敛性可 以保证,并根据此非线性广义变分原理可建立C$^1$或C$^0$类几何非线性广义杂交 元,C$^1$或C$^0$ 类精化杂交元和精化直接刚度法.指出了EAS方法用于非线性有限元分析存在的问题,即 本构关系和求解方法的限制,并对非协调元应用于非线性有限元分析提出了展望.     

TEACHING OF OPTIMAL CONTROL 1)

最优控制课程是控制科学与工程学科研究生学位必修课,同时也是力学(特别是动力学与控制方向)学位课,是一门具有理论深度和广泛工程应用的基础课。本文围绕如何提高课程教学质量、培养学生学习兴趣和创新能力的问题,对最优控制课程的教改核心、教学目标、教学内容、教学材料和教学方法等展开讨论。部分教改措施(如研讨式教学和BOPPPS教学结构)已应用于课程实践且取得良好效果。     

在工程流体力学教学中引入CFD工程案例的探讨

在长期的工程流体力学教学过程中,发现学生对这门课普遍存在畏难情绪,对复杂的理论知识掌握困难.考虑到工程流体力学的研究方法分为理论分析方法,实验方法和数值方法,而其中数值方法在传统教学中应用的较少,所以试图通过适当增加数值方法的应用来改善教学效果.随着本科生对计算机应用能力的增强以及知识面的逐渐扩展,本文提出增加结合专业背景,理论知识及软件应用的综合案例以满足当前课程及学生发展的需求.     

Free vibration characteristics of a rectangular plate carrying multiple three-degree-of-freedom spring–mass systems using equivalent mass method

This paper aims at presenting a technique to replace each three-degree-of-freedom (3-dof) spring–mass system (or substructure) by a set of equivalent masses so that the dynamic characteristics of a rectangular plate (or main structure) carrying any number of elastically mounted lumped masses may be obtained from the same plate carrying the same sets of rigidly attached equivalent masses. Because the three degrees-of-freedom (dof’s) of the substructure are embedded in its equivalent masses, the total dof of the entire vibrating system (i.e., the main structure together with all the substructures) is independent on the total number of the substructures attached to the main structure in the presented equivalent mass method (EMM). However, in the conventional finite element method (FEM), the total dof of the entire vibrating system increases by three when one more substructure is attached to the main structure. Compared with FEM, the merits of EMM are double: Firstly, since the total dof of the entire vibrating system in EMM is smaller than that in FEM, some computer storage memory may be saved. Secondly, since the dof’s for all the substructures are eliminated, the associated natural frequencies and mode shapes are excluded from those of the main structure and some effort required for the analysis of computer-output data may also be saved. It is evident that the last merits of EMM will be more predominant if the total number of substructures attached to the main structure is large.