共查询到20条相似文献，搜索用时 0 毫秒
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针对传统大型圆形贮液池力学分析方法计算复杂、精度不高的问题,用拟谱法对圆形贮液池的线弹性静力问题进行了研究.采用重心Lagrange插值多项式建立未知函数的微分矩阵,将池壁的控制方程表示为代数方程组.通过求解代数方程组,求得池壁各个离散点挠度,进而采用微分矩阵直接求得池壁内力.算例表明,该方法原理简单,易于程序实现和数值计算精度高. 相似文献
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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
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由于无网格法中大多数近似函数均为有理式, 不具有Kronecker delta性质, 因此难以精确地施加本质边界条件. 边界误差较大容易导致整个求解域求解结果精度低, 甚至引起数值不稳定现象. 文章在无网格直接配点法和稳定配点法中引入拉格朗日插值函数作为形函数, 构建了拉格朗日插值配点法(LICM)和拉格朗日插值稳定配点法(SLICM). 由于拉格朗日插值具有Kronecker delta性质, 可以像有限元法一样简单而精确地施加本质边界条件, 提高这两种方法的数值求解精度. 稳定配点法基于子域对强形式方程进行积分, 可以满足高阶积分约束, 即可以保证形函数在积分形式下也满足高阶一致性条件, 实现精确积分. 同时, 进行子域积分还可以减少离散矩阵的条件数, 从而提高算法的稳定性. 进一步提高拉格朗日插值稳定配点法的精度和稳定性. 通过数值算例验证这两种方法的精度、收敛性和稳定性, 结果表明基于拉格朗日插值的配点法的精度优于基于重构核近似的配点法, 拉格朗日插值稳定配点法的精度和稳定性均优于拉格朗日插值配点法. 相似文献
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弹性理论中的临界变分及消除方法 总被引：4，自引：0，他引：4
临界变分现象是拉氏乘子法的固有特性，钱伟长应用高阶拉氏乘子消除了临界变分现象。本文将提出一种新的方法－凑合反推法，这种方法摒充了拉氏乘子法，把拉氏乘子所在的项目一个待定函数Ｆ代替。这样构成的泛函，作者称之为试泛函。而待定函数Ｆ的识别类似于拉氏乘子的识别。通过该法可以方便地构造出各种多变量广义变分原理，并且可以消除临界变分现象。 相似文献
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Ｔｈｅｄｉｆｆｅｒｅｎｔｉａｌｑｕａｄｒａｔｕｒｅｍｅｔｈｏｄ（ＤＱＭ）ｐｒｏｐｏｓｅｄｂｙＲ．Ｂｅｌｌｍａｎ［１,２］ｈａｓｂｅｅｎｓｕｃｃｅｓｓｆｕｌｌｙｅｍｐｌｏｙｅｄｉｎｎｕｍｅｒｉｃａｌｃｏｍｐｕｔａｔｉｏｎｓｏｆｐｒｏｂｌｅｍｓｉｎｅｎｇｉｎｅｅｒｉｎｇａｎｄｐｈｙｓｉｃａｌｓｃｉｅｎｃｅ．ＢｅｃａｕｓｅｔｈｅｉｎｆｏｒｍａｔｉｏｎｏｎａｌｌｇｒｉｄｐｏｉｎｔｓｉｓｕｓｅｄｔｏｆｉｔｔｈｅｄｅｒｉｖａｔｉｖｅｓａｔｇｒｉｄｐｏｉｎｔｓｉｎｔｈｅＤＱＭ,ｉｔｉｓｅｎｏｕｇｈｔｏｏｂｔａ… 相似文献
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Zikang XU Yongsheng HAN Hongliang SHAO Zhilong SU Ge HE Dongsheng ZHANG 《应用数学和力学(英文版)》2022,43(4):557-570
Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics. The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization. To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM) is proposed. The derivatives of the shear stress on the calculation path are determine... 相似文献
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张文 《应用数学和力学(英文版)》1982,3(5):731-738
This paper is devoted to the study of the whirling phenomena of flexible rotors due to dry friction. The mechanical model used here is a two-degree-of-freedom system in which the rubbing plane is not coincident with the rotating plane of the lumped mass. The characteristic equation of whirl speeds is derived and the whirling modes are obtained. The dynamic stability of each admissible whirling motion is also discussed. The results show that the whirl speeds are always higher than the critical speed of the shaft. 相似文献
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ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅＮｕｍｅｒｉｃａｌＭａｎｉｆｏｌｄＭｅｔｈｏｄ(ＮＭＭ )ｉｓａｎｅｗｎｕｍｅｒｉｃａｌａｎａｌｙｓｉｓｍｅｔｈｏｄ ,ｗｈｉｃｈｉｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆｆｉｎｉｔｅｃｏｖｅｒｔｅｃｈｎｏｌｏｇｙｉｎｍａｎｉｆｏｌｄａｎａｌｙｓｉｓ.ＩｔｄｉｆｆｅｒｓｆｒｏｍＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｉｎｔｈａｔｔｈｅｆｉｎｉｔｅｃｏｖｅｒｓｏｆＮＭＭａｒｅｃｏｎｓｉｓｔｉｎｇｏｆｍａｔｈｅｍａｔｉｃａｌｃｏｖｅｒｓａｎｄｐｈｙｓｉｃａｌｃｏｖｅｒｓａｎ… 相似文献
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《Acta Mechanica Solida Sinica》2024,37(2)
Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability.In this work,we develop an explicit asynchronous variational integrator(AVI)for inelastic non-frictional contact problems involving a plastic solid.The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously.This asynchrony makes the AVI highly efficient in solving such bi-material problems.Taking advantage of the AVI,the constitutive update is locally performed in one element at a time,and contact constraints are also enforced on only one element.The time step of the contact element is subdivided into multiple segments,and the fields are updated accordingly.During a contact event,only one element involving a few degrees of freedom is considered,leading to high efficiency.The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening.The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency. 相似文献
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付宝连 《应用数学和力学(英文版)》1996,17(1):38-44
ＦｕＢａｏｌｉａｎ（付宝连）（ＲｅｃｅｉｖｅｄＮｏｖ．２２,１９９３;ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩ... 相似文献
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In this paper, the unsteady and non-homoentropic flow in exhaust system of diesel engine is analysed and calculated by means of characteristic method. This paper makes proper treatment in calculation, particularly in calculation of boundary conditions, then the calculation program obtained is rather common and the convergence of calculation is faster too. Finally, in this paper, we take exhaust system of 6135 turbocharged diesel engine for an example and make numerical calculation for it, The results obtained are quite satisfactory. 相似文献
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对于初始几何缺陷的功能梯度梁的振动问题,基于功能梯度材料的细观结构模型,采用幂函数模拟材料组分沿梁厚度方向的变化规律;基于Euler–Bernoulli梁理论,从几何方程和Marguerre应变得到了轴向应变的表达式,利用Hamilton原理推导了初始几何缺陷的功能梯度梁的运动微分方程,并进行无量纲化;运用微分求积法对无量纲振型微分方程以及边界条件进行离散,得到了特征方程;最后,分析了初始几何缺陷的功能梯度梁的梯度指标、初始的几何曲率、边界约束对其无量纲固有频率和振型的影响。
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用AUTODYN动力学软件对装药在混凝土介质靶中爆炸作数值仿真,研究了不同的网格描述方法,以及网格划分方法对计算结果的影响。通过实际算例比较了Lagrange算法和SPH算法以及不同的网格划分细度对靶径向、轴向不同距离的最大冲击压力、靶背过载以及损伤区、炸坑大小的模拟计算结果。分析得到了混凝土介质靶中爆炸问题数值仿真的合适算法,即拉氏算法对炸点近处的较高的最大冲击压力有较好的敏感能力,SPH算法对仿真计算爆坑形态以及抛掷体速度等具有明显的优势。对于算例问题,拉氏算法10 mm网格和SPH算法3 mm粒子即可满足一定的计算精度。 相似文献
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A high‐order triangular discontinuous Galerkin (DG) method is applied to the two‐dimensional oceanic shallow water equations. The DG method can be characterized as the fusion of finite elements with finite volumes. This DG formulation uses high‐order Lagrange polynomials on the triangle using nodal sets up to 15th order. Both the area and boundary integrals are evaluated using order 2N Gauss cubature rules. The use of exact integration for the area integrals leads naturally to a full mass matrix; however, by using straight‐edged triangles we eliminate the mass matrix completely from the discrete equations. Besides obviating the need for a mass matrix, triangular elements offer other obvious advantages in the construction of oceanic shallow water models, specifically the ability to use unstructured grids in order to better represent the continental coastlines for use in tsunami modeling. In this paper, we focus primarily on testing the discrete spatial operators by using six test cases—three of which have analytic solutions. The three tests having analytic solutions show that the high‐order triangular DG method exhibits exponential convergence. Furthermore, comparisons with a spectral element model show that the DG model is superior for all polynomial orders and test cases considered. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is used to discretize the transmission line. The nonlinear dynamic system equation is solved with the Newmark time integration method and the Newton-Raphson nonlinear iteration. Numerical examples demonstrate the efficiency of the presented method and the developed finite element program. A new possible galloping mode, which may reflect the saturation phenomenon of a nonlinear dynamic system, is discovered under the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one. 相似文献
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Introduction Meshlessmethodsarenewmethodsofnumericalcomputationwhichhavebeendeveloped rapidlyinrecentyears.Inthesemethods,onlynodesareneeded,meshinformationistotally unnecessary.Thiscanavoidorpartlyavoidthedifficultyofmeshgeneration.Duetohigh accuracyandstability,Galerkinmeshlessmethodsareappliedbroadly,butitisunavoidable tocomputetheintegrationoverthewholephysicaldomaininGalerkinweakform,whichisa greatchallengeforGalerkinmeshlessmethodsbecauseoftheabsenceofmesh.TocarryouttheintegrationinGal… 相似文献