共查询到20条相似文献，搜索用时 62 毫秒
1.
2.
本文利用拉格朗日乘子法,对弹性基础板、梁建立了一个以挠度w及地基反力P为两变量的广义变分原理,它的泛函的驻值等价于基础板,梁的一组由微分-积分方程构成的基本方程及其边界条件。 相似文献
3.
首先简化了空间变分原理的数学结构，据此表明子空间变分原理存在一定的奇异性，并提出消除奇异性的修正子空间变分原理。作为应用，计算了单材料多种截面的剪切系数并与Ｃｏｗｐｅｒ解做了比较，结果表明修正后的子空间变分原理是正确的。我们还进一步计算了一个夹层梁在Ｃｏｗｐｅｒ意义下的剪切系数，说明了子空间变分原理复杂截面的能力。 相似文献
4.
本文在文献[1]和[2]的基础上建立并论证了耦合热弹性问题的分区变分原理及其分区广义变分原理 相似文献
5.
模糊变分原理是模糊有限元重要的理论基础之一,模糊有限元的研究已经比较成熟了,然而关于模糊变分原理的研究却非常少.为研究复固有频率问题的模糊变分原理,首先介绍了一些模糊数学的概念,之后推导了非保守系统的拟Hamilton变分原理.接着通过将模糊参数引入到拟Hamilton变分原理,推导了复固有频率问题的模糊变分原理.作为模糊变分原理的应用,又推导了模糊有限元法.该方法可以直接得到问题的模糊解.与传统的模糊有限元方法相比,它避免了先将模糊参数转化为区间形式求解,之后再由区间解构造模糊解的过程.因此,该方法可以很大程度上减少计算量.最后通过数值算例表明了所提方法的可行性. 相似文献
6.
7.
本文证明了等价变分原理的泛函,实质上都只相差某种加权残差项,这也就表明了,在已知的泛函后附加加权残差项,是建立等价变分原理最简便的方法. 相似文献
8.
9.
10.
11.
首先改进文[1]的互补变分原理。再建议一种较为普遍性的方法,导出精确的边界积分方程。最后给出变分有限元及边界元解,算例证实有限元格式及迭代方式有效。 相似文献
12.
13.
挠曲电效应是一种新兴的机电耦合效应,在微纳米尺度的传感器、致动器和俘能器方面有广阔的应用前景．本文基于挠曲电材料的变分原理和电吉布斯自由能,推导了表面覆盖电极的挠曲电悬臂梁在电学开路条件下的机电耦合动力学控制方程和相应的力电边界条件．进一步获得了求解电学开路条件下挠曲电悬臂梁自振频率的超越方程．以聚偏氟乙烯(PVDF)材料为算例,讨论了挠曲电系数、末端质量块和梁尺寸对结构自振频率和电学开路/短路条件下结构自振频率有效频移的影响．计算结果表明,挠曲电系数的增大会提高梁的自振频率;末端质量的增大可以降低梁的自振频率,并且末端质量块的转动效应对悬臂梁自振频率的影响很小;悬臂梁结构的有效频移随着结构尺寸减小而增加,并在某一厚度尺寸趋于饱和值． 相似文献
14.
金伏生 《应用数学和力学(英文版)》1992,13(6):565-575
We first establish the rigorous field equations of the two continuous stages before and after entering water. Then correspondently, we obtain the specific variational principles, bounded theorems, and boundary integral equations of the second stage problems. The existence of solutions are proved and the scheme of solving the solutions are provided. Finally, as a numerical example, the ship's wave resistence problem is used to demonstrate the specific application of the second stage problems and its accuracy. Then we provide a rigorous and sound theoretical basis of variational finite element method and boundary element method for calculating the accurately fundamental equations. 相似文献
15.
From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. 相似文献
16.
Lian‐Zhi Yang Liangliang Zhang Lianying Yu Minzhong Wang Yang Gao 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2016,96(1):67-77
Based on the linear piezoelectric theory, three kinds of displacement boundary conditions are used to study the deformations of piezoelectric cantilever beams. The first two conditions are conventional simplified displacement boundary conditions, and the third one is an improved boundary condition determined by the least‐squares method. Two load cases and six slenderness ratios of cantilever beams are investigated. Solutions are given by both the conventional boundary conditions and the improved boundary condition, and are then compared with solutions by finite element method. Results from the improved boundary condition are found to be much better than those from the conventional displacement boundary conditions especially for short beams. Among the three displacement boundary conditions of the fixed end, the boundary condition determined by the least‐squares method is proved to be the most effective boundary condition. 相似文献
17.
耦合热弹性接触问题的变分原理 总被引：1，自引：0，他引：1
本文给出了考虑库伦摩擦力的热弹性接触问题的一个变分原理，该变分原理在约束条件Ｐｎ≥０和－μＰｎ≤Ｐｔ≤μＰｎ下，在接触边界上自动给出导热条件及剩余互补条件等。从它出发将接触弹性体离散后可直接进行二次规划求解。文中特地引进了因子β，它计及了接触问题中的热量散失和功率损耗 相似文献
18.
陈惟荣 《应用数学和力学(英文版)》1987,8(10):957-967
An input-output equation of the general spatial 7R mechanism is derived in this paper by using the method in [1] and applying the rotation matrices. The result is the same as [2], but the process of derivation is simpler. Applying the character of rotation matrices, it is not difficult to obtain the recurrence formulas of direction cosines of Cartesian unit vectors, to calculate the scalar products and triple products of these unit vectors, and to derive the 6th constraint equation. Moreover, an algorithm, which consists of successive applications of row transformation and expansion based on Laplace’s Theorem, is given to evaluate the 16 × 16 determinant according to its characteristic, so that the evaluation is much simplified. 相似文献
19.
20.
黄泊 《应用数学和力学(英文版)》2003,24(5):576-584
IntroductionThemethodofconvolution[1- 3]canbeusedinthestudyofpiezoelectricmaterial.Piezoelectricmaterialisoneoftheimportantsmartmaterials,usedinnovelsmartstructure .ThedynamictheoryforthermopiezoelectricelastomediawassearchedbyNowacki[4 ,5 ],Chandrasekharaiah[6 ]andIesan[7].However,region_wisevariationalprinciplesinlinearthermopiezoelectricelastodynamicshavebeennotestablishedsystematically .AlthoughLuoenandKuangJun_shang[8]havedevelopedsimplifiedGurtin_typevariationalprinciplesinlinearther… 相似文献