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1.
影响函数与有限元应力计算   总被引:3,自引:1,他引:2  
用有限元法得到位移场后,总要计算应力场。通常的做法是对位移进行微商计算应变,再根据应力-应变关系计算应力。有限元位移计算的精度比较高,但通过用位移微商来计算应力,精度会大大降低。本文利用Hamilton对偶体系的已有成果,解析求解位移和应力的影响函数,利用有限元法计算得到的位移和节点力,通过功的互等定理,可以求得一点的应力值。因影响函数是分析解,而且计算应力时不必进行微商,应力精度大幅提高。数值结果表明该方法是可行的和有效的。由该方法编制成的计算程序,可作为有限元通用程序应力计算的一个模块,将较大地提高有限元应力计算的精度和稳定性。  相似文献   

2.
引入人工压力变量,将弹性本构方程以应力、应变和压力表达,建立求解不可压缩平面弹性问题的位移-压力方程和不可压缩条件方程的耦合偏微分方程组。利用张量积型重心Lagrange插值近似二元函数,得到计算插值节点处偏导数的偏微分矩阵。采用配点法离散不可压缩弹性控制方程,利用偏微分矩阵直接离散弹性力学控制方程为矩阵形式方程组。利用插值公式离散位移和应力边界条件,将离散边界条件与离散控制方程组合为新的方程组,得到求解弹性问题的过约束线性代数方程组;利用最小二乘法求解线性方程组,得到弹性力学问题位移数值解。数值算例验证了所提方法的数值计算精度为10-14~10-10。  相似文献   

3.
提出数值分析平面弹性问题的位移-应力混合重心插值配点法。将弹性力学控制方程表达为位移和应力的耦合偏微分方程组,采用重心插值近似未知量,利用重心插值微分矩阵得到平面问题控制方程的矩阵形式离散表达式。使用重心插值离散位移和应力边界条件,采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,应用最小二乘法求解过约束方程组,得到平面弹性问题位移和应力数值解。数值算例结果表明,重心Lagrange插值方法的计算精度可达到10~(-10)量级。位移-应力混合重心插值配点法的计算公式简单、程序实施方便,是一种高精度的无网格数值分析方法。  相似文献   

4.
本文用增量牛顿-来福逊(Newton-Rophson)法完成了频率匹配器的应力分析。首次用有限单元法解决了可以简化为平面应变型的橡胶构件应力计算问题,用应变能函数的概念推导了全部计算公式,给出了橡胶材料的应力-应变非线性关系,应变-位移的非线性关系,不可压缩材料的求解公式。编制了适于位移、力或混合边界的FORTRAN-Ⅳ通用程序。计算结果令人满意。  相似文献   

5.
基于辛弹性力学解析本征函数的有限元应力磨平方法   总被引:1,自引:0,他引:1  
在实际工程结构的结构强度与优化等力学数值分析中,应力计算结果的精度是非常重要的。有限元法是得到最广泛应用的一类数值方法,并形成了众多通用的有限元程序系统。这些程序系统采用的几乎都是基于最小总势能的位移法,虽然其分析给出的有限元位移场具有较高的精度,但所得到的有限元应力场的精度较位移场大大降低。基于极坐标辛对偶体系所提供的平面弹性力学的解析辛本征展开解,并借用有限元程序系统所得到的节点位移,本文提出了一个应力分析的改进方法。数值结果表明,本方法给出的应力分析精度得到大幅提高,并具有良好的数值稳定性,可用于有限元程序系统的后处理,以提高应力尤其是关键区域应力的分析精度。  相似文献   

6.
基于敏度分析的拉压不同模量桁架问题的数值分析   总被引:2,自引:0,他引:2  
利用光滑函数技术,提出光滑化的拉压不同弹性模量问题的应力应变关系,与有限元方法相结合,建立了拉压不同模量一维连续体与桁架结构的数值求解模型,推导了敏度计算公式,采用Newton-Raphson算法进行求解.数值结果表明,本文算法具有较高的计算精度和收敛速度.  相似文献   

7.
高精度广义胞元法是多尺度分析复合材料模量和微观应力应变场的有效方法之一.然而,由于位移插值函数中缺少二次耦合项,很大程度上影响了复合材料局部应力、应变场,特别是剪切场的计算精度.本文通过引入二次方向耦合项,提出了一种修正的高精度广义胞元法插值函数.在施加周期性边界条件、平均应力和平均位移连续性条件后,可以确定位移插值函数中的系数.通过对多相复合材料弹性模量和局部场分析,并且与有限元分析和实验测量结果比较,验证了修正高精度广义胞元法的准确性.与高精度广义胞元相比,本文提出的修正高精度广义胞元法在不需要引入额外未知变量,不影响计算效率的前提下,对复合材料的局部应力场计算得更加准确.  相似文献   

8.
将不规则区域嵌入到规则的矩形区域,在矩形区域上将弹性平面问题的控制方程采用重心Lagrange插值离散,得到控制方程矩阵形式的离散表达式。在边界节点上利用重心插值离散边界条件,规则区域采用置换法施加边界条件,不规则区域采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法进行求解,得到整个规则区域上的位移数值解。利用重心插值计算得到不规则区域内任意节点的位移值,计算精度可到10-14以上。数值算例验证了所建立方法的有效性和计算精度。  相似文献   

9.
将不规则区域嵌入到规则的矩形区域,在矩形区域上将弹性平面问题的控制方程采用重心Lagrange插值离散,得到控制方程矩阵形式的离散表达式。在边界节点上利用重心插值离散边界条件,规则区域采用置换法施加边界条件,不规则区域采用附加法施加边界条件,得到求解平面弹性问题的过约束线性代数方程组,采用最小二乘法进行求解,得到整个规则区域上的位移数值解。利用重心插值计算得到不规则区域内任意节点的位移值,计算精度可到10-14以上。数值算例验证了所建立方法的有效性和计算精度。  相似文献   

10.
提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内与复合材料界面相交的裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了平面内各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。  相似文献   

11.
从矩阵位移法看有限元应力精度的损失与恢复   总被引:15,自引:0,他引:15  
矩阵位移法在计算杆端力时须叠加一个“固端力”项,而在有限元法中结点(应)力是直接对位移求导获得的,丢失了“固端力”一项,致使应力的精度大为下降.其实,对于一维有限元,同样可以对结点力叠加一个“固端力”项,使结点内力的精度与位移不相上下,而且这一做法几乎可以直接推广到半解析的有限元线法的二维问题中.本文简要介绍这一最新研究的思路、做法和一些初步的数值结果.  相似文献   

12.
基于电子-声子相互作用的双曲两步热传导模型的超快热弹性理论,计及晶格的热传导效应,利用有限元方法研究了无限大金属薄膜在短暂激光冲击下诱导的位移、应力、应变和温度等物理量的演化特点,与已有文献比较,说明该方法的合理性与正确性.比较了计及电子热爆发力与不计电子热爆发力对位移、应力等物理量的影响,说明计及电子热爆发力的必要性...  相似文献   

13.
An approach combining least squares methods and finite element methods (FEM) is presented for subsequent photoelastic stress analysis of orthogonal 3D textile composites withR and α obtained in Part 1. Through this approach, these photoelastic stresses are obtained over a region of interest as if the composites were homogeneous materials. The least squares method is used for requiring the solution strain fields to best correlate with the distribution of the two photoelastic strain data of ɛ x − ɛ y and γ xy calculated directly from the measuredR and α. The FEM uses the homogenized composite properties to construct the nodal force equilibrium equations as constraints in the least squares formulation. As a result of combining this least squares method and FEM with lagrange multipliers, a linear system of equations is formulated with the unknown nodal displacements. Once these nodal displacements are solved, the strains and stresses can be calculated through FEM formulations. This approach is tested with the two experimental results completed in Part 1 for the aluminum and composite plates. The stresses obtained for the aluminum plate show close agreement with those obtained with the plain FEM computation. In the case of the orthogonal 3D composite plate, the local variations as observed inR and α are already necessarily eliminated from these solved photoelastic stresses. Furthermore, these stresses also match well with those computed with the plain FEM from the homogenized composite properties.  相似文献   

14.
The history of stresses and creep strains of a rotating composite cylinder made of an aluminum matrix reinforced by silicon carbide particles is investigated. The effect of uniformly distributed SiC micro- and nanoparticles on the initial thermo-elastic and time-dependent creep deformation is studied. The material creep behavior is described by Sherby’s constitutive model where the creep parameters are functions of temperature and the particle sizes vary from 50 nm to 45.9 μm. Loading is composed of a temperature field due to outward steady-state heat conduction and an inertia body force due to cylinder rotation. Based on the equilibrium equation and also stress-strain and strain-displacement relations, a constitutive second-order differential equation for displacements with variable and time-dependent coefficients is obtained. By solving this differential equation together with the Prandtl–Reuss relation and the material creep constitutive model, the history of stresses and creep strains is obtained. It is found that the minimum effective stresses are reached in a material reinforced by uniformly distributed SiC particles with the volume fraction of 20% and particle size of 50 nm. It is also found that the effective and tangential stresses increase with time at the inner surface of the composite cylinder; however, their variation at the outer surface is insignificant.  相似文献   

15.
Mohamadi  Arash  Shahgholi  Majid  Ashenai Ghasemi  Faramarz 《Meccanica》2019,54(14):2227-2246

This paper investigates the linear free vibration of axially moving simply supported thin circular cylindrical shells with constant and time-dependent velocity considering the effect of viscous structure damping. Classical shell theory is employed to express strain-displacement relation. Linear elasticity theory is used to write stress–strain relation considering Hook’s Law. Governing equations in cylindrical coordinates are derived using the Hamilton principle. Equilibrium equations are rewritten with the help of Donnell–Mushtari shell theory simplification assumptions. Motion equations for displacements in axial and circumferential directions are solved analytically concerning to displacement in the radial direction. As the displacement in the radial direction is the combination of driven and companion modes, the third motion equation is discretized using the Galerkin method. The set of ordinary differential equation obtained from the Galerkin method is solved using the steady-state method, which in practice leads to the prediction of the exact frequencies of vibration. By employing multiple scale method the critical speed values of a circular cylindrical shell and several types of instabilities are discussed. The numerical results show that by increasing the mean velocity, the system always loses stability by the divergence instability in different modes, and the critical speed values of lower modes are higher than those of higher modes. As well as the unstable regions for the resonances between velocity function fluctuation frequencies and the linear combination of natural frequencies is gained from the solvability condition of second order multiple scale method. The accuracy of the method is checked against the available data.

  相似文献   

16.
弹性薄板分析的条形传递函数方法   总被引:4,自引:0,他引:4  
提出一种用于矩形弹性薄板变形分析的条形传递函数方法.一个矩形区域首先沿某一个方向被剖分成若干个条形子域,分割这些子域的直线称为结线,在结线上定义位移函数,它是结线坐标的一维函数,结线的两个端点称为结点.为适应复杂边界条件,在边界结线上定义若干结点,该结线的位移函数用结点位移参数插值表示.每个条形子域的变形用结线位移函数和适当的插值函数(形函数)表示.结线位移函数和结点位移参数满足的平衡微分方程及代数方程由变分原理给出  相似文献   

17.
混合Trefftz有限元法反平面断裂问题的探讨   总被引:1,自引:0,他引:1  
基于修正变分原理,采用满足控制微分方程的应力和位移混合Trefftz函数,满足裂纹单元断裂性质的特殊Trefftz函数以及满足裂纹尖端条件的附加试函数,推导出混合Trefftz有限元法反平面断裂问题公式,给出应力集中因子解析表达式.同时,给出单个边裂纹、单个曲折裂纹和三个边裂纹反平面裂纹问题三个算例,探讨特殊Trefftz函数个数、破裂单元个数、高斯点数以及不同附加试函数对结果的影响.最后,将计算结果与一般有限元算法或其它方法结果进行对比,分析了混合Trefftz有限元法的精确性和高效性.  相似文献   

18.
基于电子-声子相互作用的双曲两步热传导模型,并计及晶格的热传导效应,利用有限元方法研究了无限大双层金属薄膜在短暂激光冲击下诱导的位移、应力、应变和温度等物理量的演化特点.比较了计及电子热爆发力与不计电子热爆发力对位移、应力等物理量的影响,说明计及电子热爆发力的必要性.研究有利于对微型金属器件受到强热冲击产生破坏与失效的更深层次的理解,具有一定的学术意义和工程应用价值.  相似文献   

19.
Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [9020/020/9020] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.  相似文献   

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