共查询到19条相似文献,搜索用时 62 毫秒
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变刚度结构因其能适应内力的变化而应用广泛,但图乘法不能求解变刚度结构的位移。利用Gauss求积法推导出求解变刚度结构位移的近似计算法,进一步分析了其余项和精度,该方法同样适应于等刚度结构,而且结果是精确的。通过实例分析,本方法体现了其计算精度高和计算量小等优点,内力图越复杂,其优越性越明显。 相似文献
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提出了变截面纵横弯曲梁的传递函数解法,引入状态变量,将微分控制方程及边界条件方程改写成状态空间形式,然后求解,最后的算例显示了此方法的优越性,以推广该方法。 相似文献
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从变形协调出发 ,对框架的主次梁建立了矩阵位移法的求解公式 ,该方法原理清楚、简便 ,易于编程 ,为工程设计提供实用的方法。 相似文献
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《The IES Journal Part A: Civil & Structural Engineering》2013,6(4):231-239
Functionally graded material (FGM) typically consists of two constituent materials combined together with a particular distribution. A non-linear flexural stress analysis of through-thickness functionally graded uniform slender beam, subjected to a uniformly distributed load, is studied using the versatile finite element method based on Euler–Bernoulli beam hypothesis. The von-Kármán strain–displacement relations are used to account for geometric non-linearity. Simply supported and clamped FGM beams with axially immovable ends are considered. Governing non-linear equations are obtained using the principle of virtual work. Numerical results are provided to show the effect of boundary conditions and volume fraction exponent on the non-linear structural behaviour, in terms of the strains and stresses, of the FGM beams, for the first time. A shift in the neutral axis, from the mid-thickness of the beam, is observed due to the large transverse deflections, for the homogenous as well as the FGM beams. The through thickness variation of the axial stress is observed to be non-linear for the FGM beams contrary to that of the homogenous beams, for which the axial stress variation is linear. The through thickness sudden change in the material properties, governed by higher values of volume fraction exponent, results in a steep gradient in the axial stress variation through the thickness of the FGM beam. 相似文献
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Problems related to the vibrations of axially moving flexible beams made of functionally graded materials are addressed. The problem of an axially moving beam may be interpreted as a telescopic system in which the mass is not constant, the mechanism of elastic deformation is transverse bending. A thin-walled beam with annular cross-section is analyzed, in which a continuously graded variation in the composition of ceramic and metal phases across the wall thickness with a simple power law is considered. In this paper a finite element scheme is employed to obtain numerical approximations to the variational equation of the problem. Normally, finite element approaches use fixed-size elements, however, for this kind of problems the increase of the number of elements, step by step as the mass enters, is a cumbersome task. For this reason an approach based on a beam-element of variable domain is adopted. The length of the element is a prescribed function of time. Results highlighting the effects of the beam flexibility, tip mass and material constituents on the dynamics of the axially moving beams are presented and the corresponding conclusions are given. 相似文献
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Vibrations of non-uniform and functionally graded (FG) beams with various boundary conditions and varying cross-sections are investigated using the Euler-Bernoulli theory and Haar matrices. It is assumed that the cross-section and material properties vary along the beam in the axial direction. The system of the governing equations is transformed with the aid of a set of simplest wavelets. To validate the present results, the non-homogeneity of the beams is discussed in detail and the calculated frequencies are compared with those of the existing literature. The results show that the Haar wavelet approach is capable of calculating frequencies for the beams with different shapes, rigidity, mass density, small or large translational and rotational boundary coefficients. The advantage of the novel approach consists in its simplicity, accuracy and swiftness. 相似文献
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Van Chinh NGUYEN Trung Thanh TRAN Trung NGUYEN-THOI Quoc-Hoa PHAM 《Frontiers of Structural and Civil Engineering》2022,16(12):1599
This article aims to propose a finite element formulation based on Quasi-3D theory for the static bending analysis of functionally graded porous (FGP) sandwich plates. The FGP sandwich plates consist of three layers including the bottom skin of homogeneous metal, the top skin of fully ceramic and the FGP core layer with uneven porosity distribution. A quadrilateral (Q4) element with nine degrees of freedom (DOFs) per node is derived and employed in analyzing the static bending response of the plate under uniform and/or sinusoidally distributed loads. The accuracy of the present finite element formulation is verified by comparing the obtained numerical results with the published results in the literature. Then, some numerical examples are performed to examine the effects of the parameters including power-law index k and porosity coefficient on the static bending response of rectangular FGP sandwich plates. In addition, a problem with a complicated L-shape model is conducted to illustrate the superiority of the proposed finite element method. 相似文献
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本文借助于正则化理论,通过添加稳定泛函μΩ(z)=μ^2‖xk-xk-1‖^2,结合修正高斯-牛顿法,构造了非线性最小二乘问题正则化修正高斯-牛顿法求解公式;解决了普通修正高斯-牛顿法在迭代过程中其Jacobian矩阵是秩亏或者严重病态导致的不能收敛的问题;给出了非线性秩亏自由网平差的正则化修正高斯-牛顿法步骤;最后以几个经典非线性最小二乘问题为例进行了数值实验,说明了本文所提方法的正确性和适用性。 相似文献
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《Planning》2015,(2)
针对功能梯度材料物性参数随坐标变化的特点,基于Trefftz完备解提出了求解功能梯度材料热传导问题的有限梯度元方法。首先,利用变量代换推导出指数型、二次型和三角型功能梯度材料稳态热传导问题的Trefftz完备解;然后,利用Trefftz完备解对单元内部的温度场进行插值,构造出可自然模拟材料梯度属性的梯度单元,在该基础上建立混合Trefftz有限梯度元法求解功能梯度材料的稳态热传导方程;最后,采用混合Trefftz有限梯度元法对典型功能梯度材料板的温度分布进行数值模拟,以验证该方法的正确性和有效性。 相似文献
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为了更有效地求解三维轴对称功能梯度材料瞬态热传导问题,对无网格自然单元法应用于此类问题进行了研究,并发展了相应的计算方法。基于几何形状和边界条件的轴对称性,三维的轴对称问题可降为二维平面问题。为了简化本质边界条件的施加,轴对称面上的温度场采用自然邻近插值进行离散。功能梯度材料特性的变化由高斯点的材料参数进行模拟。时间域上,采用传统的两点差分法进行离散求解,进而得到瞬态温度场的响应。数值算例结果表明,提出的方法是行之有效的,理论及方法不仅拓展了自然单元法的应用范围,而且对三维轴对称瞬态热传导分析具有普遍意义。 相似文献
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《Planning》2014,(2)
传统配点法在求解动力学问题时会存在误差随时间累积的问题,而无网格径向基函数配点法在全域内采用具有无限连续性的径向基函数作为近似函数,结合配点法构建方程,通过最小二乘法进行求解。无网格径向基函数配点法不仅在数值计算过程中不需要任何网格,是真正的无网格法,而且易于离散,精度高,不需要积分,计算效率高;径向基函数的近似函数仅与距中心点的距离有关,非常适宜于求解三维问题。对于这种方法,本文先离散空间域,然后再离散时间域,并在每一时间步内施加边界条件,来分析三维功能梯度材料板的静力和动力问题,据此可解决传统配点方法在求解动力问题时误差随时间累积的问题。数值分析表明,材料性能呈梯度分布会导致其力学性能在梯度方向呈现非线性变化,不同的梯度分布模式会导致力学性能非线性变化的幅度不同。 相似文献