基于多弹簧模型的空间梁柱单元(Ⅱ):参数分析

为模拟地震作用时杆件在变动轴力和双向弯曲的耦合特点,基于简化纤维模型的多弹簧单元模型近年被广泛应用.本文作者在相关论文中提出了考虑剪切变形弹塑性刚度影响的多弹簧模型空间梁柱单元,杆件的计算模拟精度除了取决于单元模型之外,还决定于两个重要参数:弹簧位置及个数布置、塑性区长度,本文将针对其进行参数分析并提出合理建议取值.本文最后还提出了模拟杆件残余应力的合理弹簧布置方式.     

基于多弹簧模型的空间梁柱单元(II):参数分析

为模拟地震作用时杆件在变动轴力和双向弯曲的耦合特点,基于简化纤维模型的多弹簧单元模型近年被广泛应用。本文作者在相关论文中提出了考虑剪切变形弹塑性刚度影响的多弹簧模型空间梁柱单元,杆件的计算模拟精度除了取决于单元模型之外,还决定于两个重要参数:弹簧位置及个数布置、塑性区长度,本文将针对其进行参数分析并提出合理建议取值。本文最后还提出了模拟杆件残余应力的合理弹簧布置方式。     

基于点球弹簧修匀法的混合网格变形并行算法A parallel algorithm for hybrid mesh deformation based on Vertex-Ball Spring Smoothing

针对二维/三维混合网格,提出基于点球弹簧修匀法的并行网格变形算法。按特定模板将混合网格中的非三角形/四面体单元分解成三角形/四面体单元。针对每个内部节点及其相邻节点建立相应的子弹簧系统,并通过增加Ball-Vertex弹簧避免弹簧系统的塌陷问题。由于点球弹簧法在计算中逐点对网格内部节点进行计算,在计算过程中具有良好的弱耦合性质,因此有利于算法并行化。在并行化时仅需对网格进行虚拟分区操作,不必进行复杂的几何分区操作,同时避免了混合网格不同单元之间的兼容性问题。该方法适用于具有复杂外形的大规模混合网格的变形问题,能够显著提高网格变形的效率,同时具有良好的适应性。     

基于点球弹簧修匀法的混合网格变形并行算法

针对二维/三维混合网格,提出基于点球弹簧修匀法的并行网格变形算法。按特定模板将混合网格中的非三角形/四面体单元分解成三角形/四面体单元。针对每个内部节点及其相邻节点建立相应的子弹簧系统,并通过增加Ball-Vertex弹簧避免弹簧系统的塌陷问题。由于点球弹簧法在计算中逐点对网格内部节点进行计算,在计算过程中具有良好的弱耦合性质,因此有利于算法并行化。在并行化时仅需对网格进行虚拟分区操作,不必进行复杂的几何分区操作,同时避免了混合网格不同单元之间的兼容性问题。该方法适用于具有复杂外形的大规模混合网格的变形问题,能够显著提高网格变形的效率,同时具有良好的适应性。     

三角形截面梁柱构件的三维等效弹簧计算模型

传统有限元在分析梁柱构件时一般采用常应变单元和双线性单元,但此类单元在梁柱构件受弯分析中计算精度不是很高.本文根据梁柱构件的力学性能,在三维连续介质体受到轴向变形和弯曲变形的状态下,利用其轴向变形和弯曲挠度相同,得到具有相同宽度和高度且刚度等效的超静定桁架力学模型.然后,通过桁架杆的截面参数求得弹簧的刚度系数,从而得等效弹簧元模型.本文提出的等效弹簧模型计算方法简单,便于扩展到更为复杂的构件分析中.     

基于多弹簧模型的空间梁柱单元(Ⅰ):理论模型

引入多轴应力状态下的塑性应力-应变关系理论,在单元模型中考虑了弹塑性区域剪切变形对单元的弹塑性刚度影响,推导了考虑剪切变形弹塑性刚度影响的多弹簧模型的空间粱柱单元刚度矩阵,为整体钢框架结构的弹塑性动力分析奠定了单元基础.     

基于多弹簧模型的空间梁柱单元(I):理论模型

引入多轴应力状态下的塑性应力-应变关系理论,在单元模型中考虑了弹塑性区域剪切变形对单元的弹塑性刚度影响,推导了考虑剪切变形弹塑性刚度影响的多弹簧模型的空间梁柱单元刚度矩阵,为整体钢框架结构的弹塑性动力分析奠定了单元基础。     

有限元计算中疏密网格过渡方法研究

工程计算中出于节省计算量的目的,往往需要在一个有限元模型中布置粗细不同的网格。为保证计算结果的准确性,必须保证网格突变情况下的位移协调问题。本文工作之一是在强天驰界面过渡单元的基础上,引入虚拟节点和子单元,在子单元中应用节理元思想,提出了基于最小势能原理的弹簧节理单元法。简化了积分运算,避免了精度要求极高的坐标转换,从而提高了方法的精度和实用性;二是提出了基于位移约束的主从自由度法,简便实用,只需简单的矩阵运算即可实现。两种方法均实现了不同尺寸网格间位移的协调性和刚度的匹配,从而使之满足有限元收敛准则,且生成的刚度阵具有对称性及带状性。算例证明两种方法精度良好,并可方便地应用于求解大规模工程问题。     

具有半刚性节点性质的平面刚架弹簧单元的研究

联合应用力法与逐段刚化法推导出具有半刚性节点性质的弹簧节点梁单元和平面刚架弹簧单元的单元刚度方程. 该方法具有物理概念清楚,推导过程简便、巧妙的特点. 本文所建立的弹簧节点梁单元和平面刚架弹簧单元可以应用在具有半刚性节点性质的工程结构的承载力分析与计算中.     

弹簧地基上大直径单桩海上风机的一阶自振频率

自振频率是海上风机前期动力设计的主要难点之一,计算精度要求极高,而桩-土相互作用对自振频率影响显著。目前,针对桩-土相互作用普遍采用弹簧地基简化模型,为对比分析不同弹簧地基简化模型的准确性和精度,本文采用回传射线矩阵法,建立固定端、单弹簧、双弹簧和三弹簧这4种地基简化模型,基于Bernoulli-Euler梁理论和Timoshenko梁理论,求解风机系统的自振频率,并与风机基频实测值作对比,进一步分析三弹簧简化地基模型中地基旋转刚度、地基耦合刚度和地基水平刚度对风机系统基频的影响。研究结果表明,桩-土相互作用不可忽略,三弹簧地基简化模型计算风机系统基频精度最高;地基刚度对风机系统基频的敏感性次序为,地基耦合刚度>地基旋转刚度>地基水平刚度;当地基旋转(水平)刚度较小时,地基耦合刚度与地基旋转(水平)刚度的耦合效应对风机系统的基频影响较大;地基耦合刚度与地基旋转刚度的耦合效应对风机系统基频的影响程度大于地基耦合刚度与地基水平刚度的耦合效应。     

正交切削过程的刚塑性有限元算法及其实现

对刚塑性有限元用于正交切削分析中的切屑与基体材料分离准则、切屑与前刀面脱离判据等关键技术问题进行了系统的研究;建立了求解该问题的刚塑性有限元基本方程,给出了单元刚度矩阵和节点载荷列阵的详细算法以及金属大变形过程中网格畸变问题的处理技术。利用自行开发的正交切削模拟计算程序,对铝合金ZL-301创削过程进行了全程模拟,计算结果与试验结果吻合。     

Exact shell solutions for conical springs

In this article, the equations of equilibrium of conical disk springs of thin and moderate thickness are obtained through the variational principles for thin-walled and thick-walled conical shells. The closed form analytical solutions based on the common deformation hypotheses for the equations of thin- and thick-walled truncated conical shells were achieved. The results of calculations of reaction forces, based on analytical formulae, were compared with the results of finite element analysis, demonstrating the good accuracy of the derived formulae. The theory is extended to incorporate the anisotropy of the material. The problem for optimal anisotropy is solved. The minimal stiffness of the spring is achieved, if the upmost modulus of the orthotropic material is in the meridional direction. Analogously, the highest stiffness is attained, if the maximal elastic modulus circumferentially oriented. Engineering applications of the current theory potentially include Bellville springs and slotted disk springs with moderate flatness for automotive and industrial applications.     

A finite element model for linear viscoelastic behaviour of pultruded thin-walled beams under general loadings

A finite element model for orthotropic thin-walled beams subject to long-term loadings is presented. The hypothesis, rather usual for thin-walled beams, of cross-sections remaining undistorted in their own planes after deformation is introduced, so reducing the number of d.o.f.’s and, consequently, the computational effort of the analysis. The model is used to perform linear viscoelastic analysis of prismatic beams with general cross-sections, i.e., open, closed or multi-cell. As far as the constitutive viscoelastic law is concerned, a generalized linear Maxwell model is adopted. Making use of the exponential algorithm, differential equations are written in incremental form and integration is performed adopting time intervals of variable length. Numerical examples are finally presented, concerning glass-fibre pultruded shapes under long-term loadings. Displacement evolution with time and stress redistribution adopting different creep laws are presented. Convergence features of the proposed finite element and time integration procedure are also shown.     

The interaction integral for fracture of orthotropic functionally graded materials: evaluation of stress intensity factors

The interaction integral is an accurate and robust scheme for evaluating mixed-mode stress intensity factors. This paper extends the concept to orthotropic functionally graded materials and addresses fracture mechanics problems with arbitrarily oriented straight and/or curved cracks. The gradation of orthotropic material properties are smooth functions of spatial coordinates, which are integrated into the element stiffness matrix using the so-called “generalized isoparametric formulation”. The types of orthotropic material gradation considered include exponential, radial, and hyperbolic-tangent functions. Stress intensity factors for mode I and mixed-mode two-dimensional problems are evaluated by means of the interaction integral and the finite element method. Extensive computational experiments have been performed to validate the proposed formulation. The accuracy of numerical results is discussed by comparison with available analytical, semi-analytical, or numerical solutions.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.     

Nonlinear dynamic behavior analysis of an elastically restrained double-beam connected through a mass-spring system that is nonlinear

Some complex engineering structures can be modeled as multiple beams connected through coupling elements. When the coupling element is elastic, it can be simplified as a mass-spring system. The existing studies mainly concentrated on the double-beam coupled through elastic connectors, where the connector is simplified as the equivalent linear stiffness element or linear mass-spring system. Furthermore, many researches ignore rotational boundary restraints in analyzing dynamic behavior of the double-beam connected through elastic connectors, limiting their engineering generality. Considering the above limitations, this study attempts to employ the cubic nonlinear stiffness in the coupling mass-spring system and study the potential application of the mass-spring system that is nonlinear on the vibration control of the double-beam system. Using the variational method and the generalized Hamiltonian method build the corresponding system’s governing functions. Applying the Galerkin truncation method (GTM) obtains the dynamic behavior of the double-beam connected through a mass-spring system that is nonlinear. According to this study, the change of the mass-spring system that is nonlinear significantly influences the dynamic behavior of the double-beam system, where the complex dynamic behavior occurs under certain parameters of the mass-spring system that is nonlinear. Suitable parameters of the mass-spring system that is nonlinear are good at the vibration suppression at the boundary of the vibration system. Furthermore, the mass-spring system that is nonlinear can change the characteristics of the double-beam system’s kinetic energy transfer. For the vibration model established in this work, a quasi-periodic vibration state can be regarded as a sign of the occurrence of the targeted energy transfer of the double-beam connected through a mass-spring system that is nonlinear.

     

A hierarchical model for rate-dependent polycrystals

A hierarchical model of a polycrystalline aggregate of rigid viscoplastic grains is formulated, and a robust and efficient computational algorithm for its solution is proposed. The polycrystalline aggregate is modeled as a binary tree. The leaves of the binary tree represent grains, and higher tree nodes represent increasingly larger sub-aggregates of grains. The root of the tree represents the entire polycrystalline aggregate. Velocity and traction continuity are enforced across the interface between the children of each non-leaf node in the binary tree. The hierarchical model explicitly models intergranular interactions but is nevertheless comparable in computational effort to the mean field models of polycrystal plasticity. Simulations of tensile, compressive, torsional, and plane strain deformation of copper lead to predictions in good agreement with experiments, and highlight the interconnection between grain deformations and intergranular constraints. It is inferred from the results that a hybrid mean field/hierarchical model represents a computationally efficient methodology to simulate polycrystal deformation while accounting for intergranular interactions.     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

The purpose of the present work is to study the buckling problem with plate/shell topology optimiza-tion of orthotropic material.A model of buckling topology optimization is established based on the independent,con-tinuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function(PF)as filter functions are introduced to recognize the element mass,the element stiffness matrix,and the ele-ment geometric stiffness matrix.The filter functions of the orthotropic material stiffness are deduced. Then these fil-ter functions are put into buckling topology optimization of a differential equation to analyze the design sensitiv-ity.Furthermore,the buckling constraints are approximately expressed as explicit functions with respect to the design vari-ables based on the first-order Taylor expansion.The objective function is standardized based on the second-order Taylor expansion. Therefore,the optimization model is translated into a quadratic program.Finally,the dual sequence quadratic programming(DSQP)algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions(CEF and PF)are applied to solve the opti-mal model.Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.