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1.
不同模量横力弯曲梁的解析解   总被引:13,自引:0,他引:13  
选择处于平面复杂应力状态下横力弯曲梁,对结构进行了中性层的判定,推导出中性轴、正应力、剪应力、位移的计算公式,得到如下结论:对于复杂应力状态下的不同模量弹性弯曲梁,其中性轴位置与剪应力无关,因此用正应力作为判据而得到解析解,改进了以往用主应力判定中性点的多次循环的计算方法.把解析解的结果与经典力学同模量理论,以及有限元数值解进行了比较,结果表明:解析解很好地考虑了拉压不同模量的效应.还提出了对不同模量结构的计算修正以及对结构优化的思想。  相似文献   

2.
根据换热器结构形式建立了用于计算管板变形的力学模型,参考ASME Ⅷ 1计算管板的有效弹性常数,并将外筒和换热管束分别等效为会因温度和压力载荷产生轴向变形的弹簧和弹性基础.应用Ritz法建立了管板挠度的解析解,将该解析解与三个不同规模换热器的有限元分析结果进行对比.结果表明,建立的解析解与有限元分析结果吻合良好,验证了推导的管板变形解析解的正确性.研究结果对固定管板式换热器的设计有较大的指导意义.  相似文献   

3.
半刚性基层沥青路面温度场的解析理论   总被引:7,自引:0,他引:7  
本文从气象学和传热学的基本原理出发,采用解析理论建立了完全依赖气象站标准气象资料的二维非线性路面温度场的计算理论,并对不同气候条件下路面温度、土基温度及沿厚度变化的温度分布给出了相应的计算方法.  相似文献   

4.
将电磁场理论与弹性力学理论相结合,建立了描述铁磁材料在正弦电磁场中的数学模型,并对该模型一类的4阶非线性偏微分方程的解进行了讨论.给出其一阶近似后得到的线性偏微分方程的解析表达式和数值计算方法.计算结果表明,本方法是有效的.  相似文献   

5.
基于经典板理论(CPT)、一阶剪切变形板理论(FPT)以及Reddy三阶剪切变形板理论(RPT)之间,圆板轴对称特征值问题在数学上的相似性,研究了不同理论之间圆板特征值间的解析关系.将特征值问题的求解转化为代数方程的求解,并导出了不同理论之间圆板特征值的显式精确解析关系.从而。只要已知圆板特征值(临界屈曲载荷和固有频率)的经典结果,便很容易从这些解析关系中得到一阶和三阶理论下圆板特征值的相应结果。这便于工程应用,同时也可检验一阶和三阶理论下板特征值的数值结果的有效性、收敛性以及精确性等问题.  相似文献   

6.
聚合物时温等效模型有限元应用研究   总被引:2,自引:1,他引:1  
为更好地描述聚合物材料力学性能的温度相关性问题,对目前广泛应用的WLF模型进行改进研究,并引入“零时间”因子提高了粘弹性材料变温松弛模量的获取精度.在此基础上基于ABAQUS用户材料子程序UTRS将时温等效模型应用到数值计算中.根据不同温度水平下的应力松弛实验获得模型参数,并通过等速拉伸实验与数值结果的对比验证了该模型及其有限元方法的可行性及正确性.结果表明:引入“零时间”因子的变温松弛模量精度更高;改进WLF模型对复合推进剂具有更好的适用性和更高的精确度.  相似文献   

7.
采用复变函数理论和边界配置方法,分析计算了Kirchhoff扳的弯曲断裂问题.假设了位移及内力的复变函数式,它们能满足一系列的基本方程和支配条件,例如城内的平衡方程、裂纹表面的边界条件、裂纹尖端的应力奇异性质.这样,仅板边界的边界条件需要考虑.它们可用边界配置法和最小二乘法近似满足.对不同边界条件和载荷情形进行了分析计算.数值算例表明,本方法精度较高,计算量小,是一种有效的半解析、半数值计算方法。  相似文献   

8.
弹塑性杆在刚性块轴向撞击下的动力屈曲   总被引:4,自引:0,他引:4  
基于能量原理,对弹塑性杆在刚性块轴向撞击下的动力屈曲问题进行了讨论.用特征线法分析了刚性块轴向撞击是塑性直杆时应力波传播的过程.考虑了弹塑性应力波传播对屈曲的影响,建立了该问题横向扰动方程.用幂级数解法,理论上给出了该问题的级数解.分析解的性质,得到了发生屈曲时的临界条件.通过理论分析和数值计算,得到了临界速度与冲击质量、临界长度及线性强化模量间的关系.  相似文献   

9.
径向质量偏心的自由转子陀螺的漂移运动   总被引:4,自引:0,他引:4  
讨论均匀重力场中具有微小径向质量偏心的刚体定点运动,建立用状态变量描述的刚体动力学方程.对于刚体高速自旋情形应用平均法求出其近似解析积分,用以分析径向质量偏心对自由转子陀螺进动特性的影响.对径向质量偏心引起陀螺漂移现象给出物理解释,并导出陀螺常值漂移的简明的解析公式,与数值计算结果符合.  相似文献   

10.
混凝土断裂力学虚拟裂缝模型的半解析有限元法   总被引:2,自引:0,他引:2  
利用平向扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,以解析的方法推导出基于混凝土断裂力学中虚拟裂缝模型的平面裂纹解析元列式.将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和荷载混凝土平面裂纹的虚拟裂缝模型计算问题.数值计算结果表明方法对该类问题的求解是十分有效的,并有较高的精度.  相似文献   

11.
在王震鸣等人提出的各向异性多层扁壳的大挠度方程的基础上,提出了复合材料多层板壳大挠度非线性问题的迭代解法·分析了四边简支的复合材料多层矩形扁壳,与小挠度线性理论解析解及有限元非线性解进行了对比·结果表明,载荷较小并发生小挠度时,所得的大挠度解和小挠度解析解非常接近,载荷较大时,所得解和有限元非线性解非常接近·  相似文献   

12.
The size-modified Poisson–Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson–Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, Schwartz’s overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C, Fortran, and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug complex.  相似文献   

13.
As a main part of a railroad system, sleepers have important duty in conveying the load from rails to the ballast. The different situations in which the sleepers should function necessitate making them from different materials, such as various types of wood, reinforced concrete and even steel. In this work, the effects of Young’s modulus on response of railway sleeper are evaluated. As a main consideration, Winkler’s theorem is used to model the behavior of the elastic foundation. First, the response of a sleeper on a Winkler’s foundation is found. To evaluate the results of the closed form solution, a finite element model is used. Good agreement between the results of the closed form solution and the finite element model proves the validity of the results. In the next stage, the Young’s modulus is considered as a variable and the fundamental diagrams of the beam are plotted based on the variation of Young’s modulus.  相似文献   

14.
利用有限元软件建立隧道开挖正演模型,基于新奥法隧道施工现场实测围岩收敛数据,采用灵敏度分析建立了参数调整算法,利用系统识别方法对隧道围岩弹性模量及水平地应力进行了反演分析,并讨论了初始值的影响.结果表明,系统识别反演分析法具有自适应能力强、反演分析过程收敛计算稳定性好和计算速度快等优点,在隧道及地下工程领域具有广阔的应用前景.  相似文献   

15.
Time-dependent behavior of surrounding mass plays a significant role in designing underground constructions. Considering simple configuration of lined circular tunnels, a lot of solution have been proposed to this problem. However, many assume hydrostatic initial stress field, and other solutions are only applicable to simple rheological models and could not account for viscosity effect in long-term time periods. In this study, an analytical plane strain solution is proposed for lined circular tunnels under non-hydrostatic initial stress field, assuming rock mass as a viscoelastic material obeying Burgers model, while concrete lining is supposed to have linear elastic behavior. The solution which employs complex variable method combined with correspondence principle benefits from time discretization approach enabling the solution to take into account the viscosity effect in the both short-term and long-term periods of time, while predicting stress components accurately. The results obtained by the proposed solution were compared with those predicted by finite element COMSOL software which exhibited a close agreement. It was found that by increasing time both the proposed analytical solution and finite element numerical method tend to an oblique asymptote due to viscosity effect of Maxwell body in the Burgers model. Finally, a parametric analysis was performed with respect to Burgers model coefficients which showed different behavior for short and long periods of time.  相似文献   

16.
密封容器组合壳自由振动的精确解   总被引:4,自引:0,他引:4  
给出了一类密封容器组合壳自由振动问题的精确解,基于Love经典薄壳理论,导出了具有任意经线形状的旋转壳体在轴对称振动时的基本方程,组合壳结构中球壳与柱壳的连接条件是通过连接处的变形连续性和内力平衡关系得出的。问题的数学模型被归结为常微分方程组在球壳和 壳两个区间上的特征值问题。振动模态函数是由Legendre和三角函数构造出来,并且得到了精确的频率方程。所有的计算都是在Maple程序下运行的,无论是精确的符号运算还是具有所需有效数学精度的数值计算,都表明该文所编译的Maple程序是简单而有效的。固有频率的数值结果同文献中有限元法和其它数值方法的结果作了比较。作为一个标准,该文给出的精确解对于检验各种近似方法的精密度是有价值的。  相似文献   

17.
关于一个第二类变分不等式的有限元逼近   总被引:2,自引:0,他引:2  
张铁  李长军 《计算数学》2003,25(3):257-264
A new type of finite element scheme including the numerical integration modi-fication is presented for the second type variational inequality. Our methods really simplify the finite element analysis and practical calculation. The unique existence and stability of finite element solution are proved , and particularly the optimal order error estimates are derived under H^1 and L2 norms.  相似文献   

18.
The purpose of this paper is to present extended results on convergence of a method for coupling of an analytical and a finite element solution for a boundary value problem with a singularity. As an example of a singular problem we consider a solution to the Lamé-Navier equation with a singularity caused by a crack. The main idea of such an approach is to construct a continuous coupling between an analytical solution near a singularity and a finite element solution through the whole interaction interface. In this paper we present a basic theory of convergence for a method of coupling, particularly we discuss some points which show a difference to the standard theory of the finite element method.  相似文献   

19.
本文将局部投影稳定化(LPS)方法和连续时空有限元方法相结合研究对流扩散反应方程,给出稳定化连续时空有限元离散格式.与传统的时空有限元研究思路不同,时间方向利用Lagrange插值多项式,解耦时间和空间变量,降低时空有限元解的维数,具有减少计算量和简化理论分析的优点.通过引入Legendre多项式给出了有限元解的稳定性分析,进一步引进Lobatto多项式证明了有限元解的全局LL2)和局部L2Jn;LPS)范数误差估计.最后给出数值算例验证理论分析的正确性,以及稳定化格式的可行性和有效性.  相似文献   

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