基于参数二次规划与精细积分方法的动力弹塑性问题分析

给出了将参数二次规划方法与精细积分方法相结合进行结构弹塑性动力响应分析的一条新途径。基于参变量变分原理与有限元参数二次规划方法建立了动力弹塑性问题的求解方程,方法对于关联与非关联问题的求解在算法上是完全一致的。对于动力非线性方程求解则进一步采用了被线性问题分析所广泛采用的精细积分方法,推导了方法在动力弹塑性问题求解上的算法列式。所给出的数值算例在验证本文理论与算法的同时,进一步证实了精细积分方法在动力学分析中所具有的各种良好性态。     

浮基多刚体系统动力分析

引入浮体势流流固耦合理论和多刚体力学的凯恩方法对浮基多刚体系统进行动力分析。考虑入射规则波的影响和上部作业物体进行回转作业、升降作业的影响,建立了浮基多刚体系统的运动方程,讨论了浮基多刚体系统运动方程在三类情况下的求解途径。     

二维正交各向异性结构弹塑性问题的边界元分析

给出了二维正交各向异性结构弹塑性问题的边界元分析方法, 包括相应边界积分方程、内点应力公式、边界元求解格式以及弹塑性应力计算方法。在弹塑性分析中, 引入了Hill-Tsai 屈服准则, 采用初应力法和切向预测径向返回法确定实际应力状态。通过具体算例分析了二维正交各向异性结构的弹塑性应力和塑性区分布情况, 部分数值结果与已有结果进行了比较, 两者基本吻合。结果表明, 本文中给出的边界元法可以有效地用于求解二维正交各向异性结构的弹塑性问题。      

直杆塑性动力屈曲的能量准则和特征参数解

提出弹塑性应力波作用下直杆动力屈曲的定量求解方法，将临界应力和惯性指数作为一对特征参数求解．由相平衡邻位形准则得出屈曲控制方程和边界条件，由所导出的能量转换和守恒准则得出压缩波阵面上的附加约束方程，由此得出了问题的完备定解条件，从而提出了求解直杆塑性动力屈曲的特征参数方法。     

水平激励下带竖向隔板的二维矩形储箱中流体晃动研究EI北大核心CSCD

研究了水平激励下二维矩形储箱中流体的晃动,抑制晃动的装置为竖向的刚性隔板,建立了隔板在储箱自由液面处的解析模型。首先通过引入人工界面的方式,将流体域划分成若干个流体子域,使每个流体子域对应的速度势函数满足C1连续性条件。基于叠加原理,使用分离变量法求得每个流体子域的速度势的形式解,将形式解代入子域间界面与自由液面条件可得含有待定系数的级数方程,通过加权积分消去方程中的空间坐标,截断方程可得特征方程,由此可得晃动频率与模态。将水平激励下的速度势函数分解为摄动速度势与刚体速度势,将摄动速度势和刚体速度势代入自由液面的波动方程即可求得含广义坐标的动力响应方程,求解该方程可得储箱中流体的晃动响应。     

柔性框架结构动力非线性分析的刚体准则法

大跨、高层等柔性结构,其动力响应往往表现出大位移、大转动等非线性特征。动力非线性问题的分析关键在于运动方程的高效稳定求解,以及单元大转动产生的结点力增量的有效计算。动力时程分析通常采用直接积分法,但对于强非线性动力问题,直接积分法难以兼顾计算精度与稳定性。该文基于几何非线性分析的刚体准则,针对杆件结构大转动小应变的非线性问题,提出了一种新型空间杆系结构动力非线性分析的刚体准则法。该方法采用满足刚体准则的空间非线性梁单元,结合HHT-α法求解结构运动方程,并将刚体准则植入动力增量方程的迭代求解过程以计算结点力增量。通过典型柔性框架算例结果表明,该文方法可以有效分析柔性框架结构的强动力非线性行为。与高精度单元相比,该文采用的单元刚度矩阵构造简明,计算过程简洁;与商业软件所用方法相比,单元数和迭代步少,精度高,适于工程应用。     

高层筒体结构弹塑性地震反应分析的样条积层有限条法

采用三次B样条积层有限条方法对结构进行离散，推导出结构的静平衡力、惯性力、地震力及其阻尼力的节点位移的表达式，由达朗贝尔原理，得到结构的动力平衡方程，采用预校正形式的Newmark法求解结构的动力方程。另外，根据等向强化准则，处理受压区混凝土材料及钢筋材料的弹塑性本构关系；应用分布裂缝模式，解决受拉区混凝土的开裂问题，由此实现了简体结构的弹塑性地震反应分析，最后通过实例比较分析，验证了方法的正确性与高效性。     

率相关饱和多孔介质动力响应的数值分析

在基于混合物理论的多孔介质模型的基础上,将固体相视为弹粘塑性体,建立了饱和多孔介质的弹粘塑性模型。模型的基本思想是在无粘弹塑性本构关系中引入-时间参数,使固体骨架具备了粘性效应。利用Galerkin加权残值法推导得到了罚有限元格式,并采用Newmark预估校正法求解率相关饱和多孔介质的非线性有限元动力方程,此算法可以很...     

离散-连续多尺度桥域耦合动力分析方法

基于离散介质理论和连续介质理论,提出离散-连续多尺度动力耦合分析方法,不需要任何附加的过滤和阻尼就能有效地消除高频波的虚假反射。根据实际需求将计算模型划分为连续介质域和离散介质域,其中连续介质域采用有限差分网格模拟;离散介质域采用离散元颗粒模拟。为保证网格与颗粒两种不同介质之间的能量协调,引入拉格朗日乘子将离散元模型和有限差分模型之间的约束关系,通过能量势函数隐含到动力方程中,推导出多尺度域的动力控制方程。基于动力显式算法求解所建立的离散-连续多尺度动力耦合体系,在通用的离散元(PFC)和有限差分法(FLAC)软件中二次开发编制计算程序,从而实现离散-连续多尺度动力耦合算法。通过算例验证,计算结果与分别采用离散元和有限差分法所得结果一致,说明了该多尺度方法可以有效地消除高频波在离散-连续介质界面上的虚假反射现象。     

平面框架动力响应的状态空间分析

本文根据结构动力学方程，引入状态空间，导出平面框架结构动力响应问题的状态方程，并在此基础上建立了迭代计算格式，用于结构动力响应计算，数值结果表明，该方法具有较真高精度，且求解效率高。     

Nonlinear static/dynamic analysis for elasto-plastic laminated plates with interfacial damage evolution

A new analysis model, which includes the effects of interfacial damage, geometrical nonlinearity and material nonlinearity, is presented for elasto-plastic laminated plates. Based on the model, the nonlinear equilibrium differential equations for elasto-plastic laminated plates with interfacial damage are established. The finite difference method and iteration method are adopted to solve these equations. The nonlinear static and dynamic behaviors for the elasto-plastic laminated plates under the action of transverse loads are analyzed. Effects of interfacial damage on the stress and displacement distribution and nonlinear dynamic response are discussed in the numerical examples together with the comparison of nonlinear mechanical behaviors between the elastic and elasto-plastic laminated plates. Numerical results show that both the interfacial damage and plastic deformation put obvious influence on the mechanical properties of structures.     

A boundary element solution to elasto-plastic torsion of solids of revolution

A boundary element method for the solution of problems of elastic and elasto-plastic torsion of solids of revolution is proposed. The displacement and stress field produced by a circumferential ring load in an infinite elastic body are derived and used as the fundamental solution to establish the governing integral equations. For the elasto-plastic case, linear boundary elements and bilinear quadrilateral internal cells are used for discretization of these equations. In order to carry out Gaussian integrations along boundary elements and over internal cells, a method ensuring sufficient accuracy for the calculation of singular integrals is proposed. Numerical results for several problems are given.     

Elasto-plastic Analysis of Two-dimensional Orthotropic Bodies with the Boundary Element Method

The Boundary Element Method (BEM) is introduced to analyze the elasto-plastic problems of 2-D orthotropic bodies. With the help of known boundary integral equations and fundamental solutions, a numerical scheme for elasto-plastic analysis of 2-D orthotropic problems with the BEM is developed. The Hill orthotropic yield criterion is adopted in the plastic analysis. The initial stress method and tangent predictor-radial return algorithm are used to determine the stress state in solving the nonlinear equation with the incremental iteration method. Finally, numerical examples show that the BEM is effective and reliable in analyzing elasto-plastic problems of orthotropic bodies.     

Singular integral operators method for two-dimensional elasto-plastic stress analysis

The Singular Integral Operators Method is presented for the formulation of the two-dimensional elasto-plastic stress analysis. The formulation of the two-dimensional elasto-plastic problem is stated, by applying the fundamental solutions for an isotropic solid. The most interesting features of this method are the much smaller systems of equations and considerable reduction in the data required to run the elasto-plastic problem. An application is presented, to the determination of the stress field in the neighborhood of a circular hole under internal pressure in an infinite and isotropic solid. A second application is stated, to the determination of the plastic behaviour of a square block compressed by two opposite perfectly rough rigid punches in plane strain.     

梁撞击弹塑性波传播的动态子结构方法的研究

该文针对简支梁横向弹塑性撞击问题,建立动态子结构模型,推导了相应的动力学控制方程,并采用Newmark隐式积分法进行求解,将动态子结构方法应用于撞击激发弹塑性波传播问题的研究。考虑局部弹塑性接触变形,通过对撞击激发的弹塑性波传播,包括弯矩波、挠曲波、速度波和应力波传播过程的计算,研究动态子结构法分析弹塑性波的传播特征,弯曲波的弥散特征,以及塑性铰形成机理等的合理性。经过与三维动力有限元计算结果的比较表明,动态子结构方法可以合理地应用于柔性梁中弹塑性撞击瞬态波传播问题的研究。     

Localized direct boundary-domain integro-differential formulations for incremental elasto-plasticity of inhomogeneous body

A quasi-static mixed boundary value problem of incremental elasto-plasticity for a continuously inhomogeneous body is considered. Using the two-operator Green–Betti formula and the fundamental solution of a reference homogeneous linear elasticity problem, with frozen initial or tangent elastic coefficients, a boundary-domain integro-differential formulation of the elasto-plastic problem is presented, with respect to the displacement rates and their gradients. Using a cut-off function approach, the corresponding localized parametrix of the reference problem is constructed to reduce the elasto-plastic problem to a nonlinear localized boundary-domain integro-differential equation. Algorithms of mesh-based and mesh-less discretizations are presented resulting in sparsely populated systems of nonlinear algebraic equations for the displacement increments.     

Nonlinear Dynamic Analysis of Three-Dimensional Elasto-Plastic Solids by the Meshless Local Petrov-Galerkin (MLPG) Method

The meshless local Petrov-Galerkin approach is proposed for the nonlinear dynamic analysis of three-dimensional (3D) elasto-plastic problems. Galerkin weak-form formulation is applied to derive the discrete governing equations. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a unit test function and local weak-form formulation in three dimensional continua for the general dynamic problems is derived. Three dimensional Moving Least-Square (MLS) approximation is considered as shape function to approximate the field variable of scattered nodes in the problem domain. Normality hypothesis of plasticity is adopted to define the stress-strain relation in elasto-plastic analysis and the unknown plastic multiplier is obtained by the consistency condition. Von Mises yield criterion in three dimensional space is used as a yield function to determine whether the material has yielded. The Newmark time integration method in an incremental form is used to solve the final system of nonlinear second order Ordinary Differential Equations (ODEs). Several numerical examples are given to demonstrate the accuracy and effectiveness of the present numerical approach.     

Analysis of delamination fatigue growth for delaminated piezoelectric elasto-plastic laminated beams under hygrothermal conditions

A nonlinear analysis model of fatigue delamination growth for piezoelectric elasto-plastic laminated beams under hygrothermal conditions is presented. Based on the incremental elasto-plastic constitutive equations, the incremental nonlinear governing equations of the piezoelectric elasto-plastic laminated beams with delamination are derived when taking into account the hygrothermal environments, transverse shear deformation, geometrical nonlinearity and piezoelectric effect. According to the elasto-plastic fracture dynamics and J-integral theory, the energy-release-rate along the delamination is obtained. Then, applying the Paris law, the delamination growth rate is obtained and the delamination growth lengths along the delamination fronts under cyclic loads are finally determined by using the cyclic skip method. The equations are solved by the finite difference method and iterative method as a whole. Effects of voltages, variation of temperature and humidity, delamination length and depth on the energy-release-rate and delamination growth length for the piezoelectric elasto-plastic laminated beams are discussed in numerical examples.     

A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment

The reliability and limits of solutions for static structural analysis depend on the accuracy of the curvature and deflection calculations. Even if the material model is close to the actual material behavior, physically unrealistic deflections or divergence problems are unavoidable in the analysis if an appropriate fundamental kinematic theory is not chosen. Moreover, accurate deflection calculation plays an important role in ultimate strength analysis where in-plane stresses are considered. Therefore, a more powerful method is needed to achieve reliable deflection calculation and modeling. For this purpose, a new advanced step was developed by coupling the elasto-plastic material behavior with precise general planar kinematic analysis. The deflection is generated precisely without making geometric assumptions or using differential equations of the deflection curve. An analytical finite strain solution was derived for an elasto-plastic prismatic/non-prismatic rectangular cross-sectioned beam under a uniform moment distribution. A comparison of the analytical results with those from the Abaqus FEM software package reveals a coherent correlation.     

Dynamic elasto-plastic response of shells in an acoustic medium—EPSA code

A nonlinear, large deflection, elasto-plastic finite element code (EPSA) has been developed for the analysis of shells in an acoustic medium subjected to dynamic loadings. The nonlinear equations of shells are discretized with the aid of a finite difference/finite element method based upon the principle of virtual work. The resulting system of equations contains the nodal displacements as the generalized co-ordinates of the problem. The integration in time of the equations of motion is done explicitly via a central difference scheme. Shell strain-displacement relations are established by a two-dimensional finite difference scheme. The shell constitutive equations are formulated in terms of the shell stress resultants and the shell strains and curvatures. The fluid-structure interaction is accounted for by means of the doubly asymptotic approximation (DAA) expressed in terms of orthogonal fluid expansion functions. The analytically produced results satisfactorily reproduce available experimental data for dynamically loaded shells.