The generalized finite element method (GFEM) is versatile and powerful in the numerical analysis of various engineering problems. However, its application to large deformation analysis of elastoplastic solids is rare, especially in three dimensions (3D), since it suffers from singular system matrix and awkward implementation. This issue is caused by the extra degrees of freedom (DOFs) of GFEM. In this work, a nonlinear GFEM for large deformation analysis of elastic and elastoplastic solids in 3D is developed by using the extra-DOF-free enrichments proposed by Tian (2013) Updated Lagrangian (UL) formulation incorporating both geometric and material nonlinearities is employed and hyperelastic and hypoelastic–plastic constitutive models are considered. As a result of the elimination of the extra DOFs, implementation of the developed method is much more convenient than the standard GFEM and singular system matrix does not present. The capability of the proposed nonlinear GFEM in modeling three-dimensional large elastoplastic deformations is investigated by several typical examples. Numerical results demonstrate that, in comparison to the traditional finite element method, the proposed nonlinear GFEM is remarkably more accurate and stable. Particularly, in analysis of extreme deformations, the commercial software ABAQUS fails even when sophisticated elements are used, however the proposed nonlinear extra-DOF-free GFEM is still stable and converged results can be obtained.
This paper establishes a geometrically nonlinear bending analysis framework using the deep energy method and the classical laminated plate theory (CLPT) for laminated plates. Inspired by the transfer learning technique, a load applied to a laminated plate can be divided into multiple load steps. The network parameters for the current load step, with the exception of the initial step, are initialized by inheriting values from their preceding steps. Including both von Kármán and Green-Lagrange strains, the plate strains are computed using the automatic differentiation and integrated along the thickness direction per laminate plate based on the constitutive theory. By combining the outputs of neural network, the external potential energy can be obtained, and the optimized network parameters are given by minimizing the total system potential energy of the laminated plate. In order to validate the proposed approach, several numerical examples are calculated, and the present solutions are compared with those given by the literature and the Finite Element Analysis (FEA). The results show that the proposed approach is indeed feasible, can reach high levels of precision under varying loads while offering a simplified calculation strategy.
In order to solve the problems of the classical fifth-order weighted essentially non-oscillatory(WENO)scheme,such as the excessive dissipation near the discontinuity and the inaccurate preserving of the critical point,a new modified stencil approximation method is proposed.The second-order polynomial approximation of the numerical flux on each candidate sub-stencil in the classical fifth-order WENO-JS scheme is improved,and the stencil approximation reaches the fourth-order accuracy by adding a cubic correction term.The new scheme has ENO property by introducing adjustable function φ,and the theoretical analysis shows that the new scheme has accuracy-preserving property.A series of numerical examples show the efficiency of the new scheme.
In order to analyze the distortion effect of trapezoidal composite box girder with corrugated steel webs and steel bottom plates,the restraint effect of top and bottom plates on corrugated steel webs is considered.Maintain the in-plane and out-of-plane bending stiffness unchanged when the composite box girder is equivalent to a steel box girder.Based on the plate element frame method,the distortion governing differential equation is set up based on plate element frame method and the general solution of Krylov function is derived.Combined with the comparative analysis of numerical examples,the rationality of this method is verified,and the influence of web depression angle and girder height on bi-moments is studied.The results demonstrate that it is more reasonable to consider the restraint effect of the top and bottom plates on the webs than to ignore the in-plane bending stiffness of the webs completely.As distortion warping stiffness and transverse frame stiffness of box girder is greatly weakened by corrugated steel web and steel bottom plate,the distortion warping stress of traditional corrugated steel web composite box girder can reach 1.98 times that of ordinary concrete box girder.And the distortion warping stress of corrugated steel web composite box girder with steel bottom plate can reach 15.31 times of that of traditional corrugated steel web composite box girder.The bi-moment near the mid-span section changes little with the web depression angle,and the bi-moment in other sections decreases gradually with the increase of the web depression angle.The distortion bi-moment increases slightly with the increase of girder height,and its maximum position changes.
In order to study the distortion effect of a composite concrete box girder with a steel truss web,on the basis of the thin-walled box girder theory,considering the mechanical properties of the steel truss web,the improved plate element analytic method is used to establish the differential equation for distortion.The distortion analytical solution are given.A solid model through ANSYS to verify the correctness of the derived formula is established.Combined with numerical examples,the distortion stresses of a composite box girder and a traditional concrete box girder with the same cross-sectional parameters under a uniformly distributed distortion load are compared and analyzed.The influence of the beam width and the depression angle of the steel web on the distortion internal force of the composite box girder is analysed.The results show that under the same section parameters,due to the small longitudinal stiffness of the steel truss web member of the composite box girder,of which distortion warping normal stress is 1.71 times of that of the concrete box girder;the beam width has a great influence on the distortion internal force,and when the beam width increases to 4.5 m,the distortion double moment and the distortion moment increase to 3.68 times and 1.36 times respectively,and the distribution trend of the former two peaks in the longitudinal direction is gradually flat;When the depression angle of the steel web increases to 27°,the distortion double moment is reduced by about 14.3％,but it has little effect on the distortion moment.
Topology optimization of simplified convective heat transfer has been widely studied, but most existing studies are based on the finite element method (FEM); methods based on the finite volume method (FVM) have been less studied. In this paper, a topology optimization method based on FVM was proposed for a simplified convective heat transfer problem. We developed a novel adjoint sensitivity analysis method applicable to FVM, which included adjoint equations, corresponding boundary conditions, and sensitivity analysis equations. Additionally, a program for the proposed topology optimization method was developed in open field operation and manipulation (OpenFOAM) and portable, extensibletoolkit for scientific computation (PETSc). Thus, large-scale topology optimizations could be performed in parallel. Furthermore, numerical examples of the classical two-dimensional (2D) and 3D optimization problems were considered. The results verified the effectiveness and feasibility of the proposed method. The results of large-scale 3D examples show an interesting phenomenon that for the optimized designs with few features, the large-scale topology optimization is still valuable for obtaining more effective structural shapes.
陡倾滑面滑坡推力竖向分力显著,基于滑坡推力水平假定与普通抗滑桩相互作用不充分这一问题,建立锯齿形抗滑桩结构.依据梯形分布滑坡推力的假设,推导了受荷段内力计算公式,采用Winkler弹性地基理论推导了锚固段内力计算公式,并开展锯齿形抗滑桩的力学性能研究.分析表明,(1)随着滑面倾角的增加,锯齿形抗滑桩的受荷段、锚固段的弯矩、剪力以及侧应力均减小,内力减小幅度随之增大;(2)滑面倾角在20°～40°时,随着滑面倾角的增加,锚固段的理论最小长度在逐渐增加,40°时锚固段的长度为4.2 m达到最大值,且该长度仅占整个桩长35％,远小于按现行规范取得的锚固段长度最大值(1/2总桩长),桩侧摩阻力就可以完全满足竖向力学平衡;(3)将锯齿形抗滑桩与普通抗滑桩内力对比,受荷段和锚固段的弯矩减小34％、剪力减小36％及桩侧应力减小幅度大于30％,力学性能良好.
工程结构在服役期不可避免地遭受各种不确定因素的侵害,为客观科学地描述不确定因素的影响,可靠度理论得以产生和发展.但传统的可靠度分析方法囿于精度和效率等原因,难以应用于实际工程结构.近年来基于概率守恒原理,概率密度演化理论提出并得到发展.但对复杂的工程结构,效率低下等问题依然有待解决.鉴于此,本文提出两级剖分概率空间的概念,以粗剖分获得的少量代表样本构成训练集,训练Kriging模型;然后细剖分概率空间,通过训练的Kriging模型预测加密样本响应提高分析效率.基于此,结合以概率密度演化理论为基础的物理综合法,提出了 一种新的可靠度分析方法.通过对一解析系统和一幢钢筋混凝土框架结构的响应预测与可靠度分析,证明了新提出方法的精度和效率.
克服介质相变、峡谷分层且局部地形覆水导致的固有边界值难题,首次推导并得到了半覆水相变V形峡谷场地对P波激励下的散射理论解,验证理论解的正确性,探究了相变界面的有无、入射波频率和入射角对地表位移的显著影响,突出并重点强调了覆水因素对结果影响的不可忽视性.分析结果表明,(1)以经典算例为标准,对比验证了本文理论解的正确性,解释并澄清了峡谷局部可预测性的微小偏差的来源.(2)与未覆水部位相比,峡谷覆水部位表面位移显著增大;与峡谷满水状态相比,相变面的存在使位移增大的初始位置向峡谷中间移动;不同的入射波频率和入射角下,地面运动情况存在显著差异,随着入射角的增大,水平方向的位移逐渐增大,竖直方向的位移逐渐减小.本文研究可为覆水V形峡谷的长大结构多点地震动的合理输入提供基础性研究依据,兼有理论意义与应用价值.
碳纳米管作为导电相在机敏复合材料中广泛应用,但碳纳米管为团簇材料,在基体中很难均匀分散.本文考虑碳纳米管的非均匀分布特性,提出了计算碳纳米管复合材料电导率的数值方法.通过引入随机谐和函数,建立了碳纳米管体积分数的三维随机场模型.基于细观力学的有效介质理论、Mori-Tanaka方法和H-S界限理论,考虑碳纳米管之间的隧穿效应,发展了复合材料微小体积单元的电导率计算方法.在此基础上,构建了考虑碳纳米管非均匀分布的复合材料等效电导率三维有限元计算模型.数值分析结果与试验值能够很好吻合,表明这一方法可以准确计算碳纳米管复合材料的电导率.本文进一步分析了碳纳米管非均匀分布对复合材料电导率的影响.
为研究砖石古塔的动力特性及地震响应机制,以渭南慧照寺塔为对象,采用块体-灰浆分区离散方法,分别建立刚性地基条件与考虑地基-结构相互作用条件下古塔的数值模型,计算比较了塔体的动力特性;并分别按9度小震、中震和大震输入El-Centro波、Taft波和兰州人工波,计算了结构的位移和加速度反应,与相互作用系统进行比较.结果表明,考虑土-结构相互作用后,古塔结构的一阶自振频率降低5.7％,二阶频率降低45％;El-Centro波和Taft波作用下,位移和加速度响应显著增大,大震作用时,与不考虑土-结构相互作用对比,主拉应力峰值显著增加,古塔从灰浆开裂发展为砖与灰浆同时开裂;兰州人工波作用下,考虑土-结构相互作用后,主拉应力和结构开裂变形反而降低.研究结果可为古塔抗震计算与性能评估提供参考.
2023年8月21日,《计算力学学报》第八届编委会在大连召开第2次工作会议.会议由主编大连理工大学亢战教授主持.副主编西安交通大学王铁军教授,副主编大连理工大学李刚教授,副主编大连理工大学郭旭教授,编委河北工业大学韩旭教授,西北工业大学邓子辰教授,河海大学章青教授,清华大学张雄教授,厦门大学王东东教授,中科院大学王智慧教授,兰州大学刘小靖教授,湖南大学侯淑娟教授,北京理工大学廉艳平教授,大连理工大学陈飚松教授,专职副主编冯颖编审全程参加了会议,学报编辑部编辑刘燕老师列席会议.
基于微-细观随机断裂模型(MMSF)发展了一类混凝土随机疲劳损伤模型.该模型将MMSF中的微弹簧视为一能量耗散单元并考察了其跨尺度的能量耗散过程.在纳观尺度,引入速率过程理论描述裂纹的扩展速度,并基于裂纹层级模型和自相似假定完成从纳观尺度到微观尺度的过渡.由此建立了微弹簧在疲劳荷载作用下的多尺度耗能描述.此外,为了考虑疲劳加载中混凝土多条裂纹的相互影响,引入了包含损伤扩展效应和损伤愈合效应的疲劳损伤因子来修正耗能表达.通过与相关试验的对比,证明了该模型能反映疲劳荷载作用下混凝土的主要力学行为,如疲劳损伤三阶段特点、疲劳寿命的离散性和疲劳寿命随加载频率的变化趋势等.
针对结构在随机激励作用下的动力响应统计特征分析问题,提出了结构平稳和非平稳随机振动时域响应分析的多项式维数分解PDD(polynomial dimensional decomposition)法,高效地实现了结构随机振动响应统计矩和概率密度的计算.首先,采用三角级数叠加法模拟随机激励,将其中的随机相位作为结构系统的随机输入,并将结构随机振动时域响应视为关于随机相位的函数.其次,将结构响应函数采用成员函数(Component function)进行维数分解,并对成员函数进行Fourier多项式展开,从而构造出结构响应预测的PDD展开模型.最后,为了解决构造PDD展开模型时面临的高维积分问题,采用降维积分方法降低积分维度,显著提高了计算效率.在数值算例中,进行了单自由度系统和20层框架结构的随机振动时域响应分析,并将本文方法的计算结果与Monte Carlo模拟结果进行对比,验证了建立方法的精确性和高效性.
基于弯扭组合梁元对大展弦比多段折叠翼的离散突风响应特性进行了研究.首先,将平面一般梁元叠加扭转自由度得到一种新的弯扭组合梁元,建立包含折叠角参数的缩减有限元模型.其次,对片条理论进行修正以得到不同折叠角度下弯扭组合梁元上的气动力,构建多段折叠翼在离散突风作用下的动力学方程.最后,引入Laplace变换处理动力学方程中的积分微分项,得到折叠角对翼尖加速度、翼根弯/扭矩等响应的影响.一个近地面无人机三段式折叠翼的算例结果表明,机翼固有频率会随着折叠角的变化呈现非线性性态,相比舒展状态,折叠角的存在虽不能明显减小翼尖加速度,但能够有效减小翼根弯/扭矩响应.
为研究高速列车简支梁振动的问题,利用移动荷载列解析表达式的极限条件,推导了共振与消振速度.从自由振动幅值的角度,证明了桥梁振动主要由一阶模态贡献,且随着车速的增加,二阶模态对 自由振动的贡献逐渐增大,而更高阶的模态贡献量可忽略不计.提高桥梁阻尼能起到抑振的作用,但会加剧车辆驶离桥后的 自由振动.以20 m和32 m的两座简支梁桥为算例,从自由振动的幅值和相位出发,阐明 了在特定的速度下,发生共振与消振的主要原因是轴载激励的 自由振动之间出现叠加、抵消或抑制的现象.当共振速度与消振速度重合时,消振先于共振发生.比较移动轴载解析值与车-轨-桥耦合有限元模型的计算值,结果表明,移动轴载模型能有效预测桥梁的位移时程,但分析桥梁的加速度响应时,有必要考虑车-轨-桥之间的动力耦合效应.
非线性系统的随机振动分析一直是结构动力学领域中的难点,已有一些研究表明基于矩等效的线性化方法在功率谱预测上会得到不恰当的分析结果;另一方面,由于不确定性在实际工程中普遍存在,如果同时考虑非线性和不确定性,更是显著增加了问题难度.本文以具有非线性非理想边界梁为研究对象,基于梁模型的动力学微分方程推导了对应的广义频响函数,并应用Volterra级数理论建立了非线性系统随机振动的谱分析方法,最后,结合蒙特卡洛抽样方法计算了具有参数不确定性非线性梁响应功率谱的均值和方差,讨论了不确定性对结构随机振动响应统计特征的影响.
基于连续介质或者离散裂隙假设,含裂隙的多孔介质渗流问题有多种数学力学模型.受物理界面的启发,提出一种新的有限裂隙连续介质力学模型,可以为宏观裂隙-多孔介质内的流体输运问题等提供近似计算方案.该模型属于一类双重介质模型,将曲面上低维度的流场转化为三维空间的流场,并且与连续的多孔介质的流场耦合,在数学上表示为统一的输运控制方程和初始边界条件.这个近似模型为不方便实施高维度-低维度耦合求解的数值计算方法提供新的模拟思路,如光滑粒子流体动力学等无网格粒子类方法.
为改善传统卡尔曼滤波KF(Kalman filter)算法在过程噪声方差和测量噪声方差未知的情况下响应重构精度降低甚至发散的问题,提出了 一种基于新息自适应卡尔曼滤波IAKF(innovation-based adaptive Kalman fil-ter)算法的多类型响应重构方法.首先根据新息统计特性对卡尔曼滤波增益和状态估计误差协方差矩阵进行实时自适应调整;然后利用有限测点的加速度传感器的测量数据,结合模态法对结构各个位置的加速度、速度、位移以及应变进行响应重构;最后对起重机桁架和简支梁分别进行数值模拟和试验分析.结果表明,该方法能够有效地调整过程噪声方差并估计测量噪声方差,未测点的重构响应时程曲线与计算响应或测量响应时程曲线吻合良好.
子集模拟是当前可靠度计算领域常用的估计算法,相比于直接蒙特卡罗积分法,极大减少了函数调用的次数.子集模拟法一般使用单一采样器,然而不同采样器适用范围不同.如使用单一椭圆切片采样器,其遍历性较好但函数调用次数较多;而使用单一自适应条件采样时,其采样效率较高但样本容易陷入局部极值.单一采样器由于本身特性面对不同问题时失效概率的积分结果可能出现偏差,模拟效果不稳定.本文首次提出了一种混合采样子集模拟法,在子集模拟的前几层使用椭圆切片采样,此时失效区域收缩程度有限,函数调用次数在可接受的范围内,样本经过采样扩充后能充分探索参数空间,更有效地检测出所有失效区域.当失效区域收缩至一定限度后,使用 自适应条件采样,此时种子样本继承了前几层样本较低的相关性,并在此基础上通过自适应条件采样更高效地增殖样本.本文通过四个模拟算例多种维度下的数值积分验证了该算法具有椭圆切片采样器较好的遍历性,同时采样效率位于椭圆切片采样与 自适应条件采样之间,对于不同问题拥有良好的通用性.
