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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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In this paper, the Hu-Washizu generalized variational principle isextended to nonlinear elastodynamics with five independent fields. The twokinds of framework of functional, the potential energy and complementaryenergy expressions containing the subsidiary conditions with Lagrangemultipliers are suggested. According to the principle of stationaryfunctional, we have the governing equations and Lagrange multipliersdetermened by the results of variation. The generalized sub-region mixed andhybrid variational principle in nonlinear elastodynamics is presented.Supported by National Natural ScienceFoundation of China. 相似文献
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板弯曲与平面弹性问题的多类变量变分原理 总被引:3,自引:0,他引:3
进一步完善板弯曲与平面弹性问题的多类变量变分原理,给出了相关边界积分项的具体表达式.多类交量变分原理涵盖了平衡、应力函数、应力、位移一应变、协调和物性共五大类基本方程和所有边界条件,是一个具有更加广泛意义的变分原理. 相似文献
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Bohua SUN 《应用数学和力学(英文版)》2022,43(4):537-546
There is an open question,namely Chien’s question,in construction of a generalized functional in elasticity,i.e.,why the stress-strain relation can still be derived from the Hu-Washizu generalized variational principle while the Lagrangian multiplier method is applied in vain?This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics.This investigation finds that as long as the functional has one of the comb... 相似文献
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Hu Haichang 《Acta Mechanica Sinica》1986,2(2):129-137
The fundamentals for the correct use of the method of Lagrange multiplier are presented and illustrated by examples. Some
misunderstandings of the method are clarified. Equivalent variational principles are defined. It is pointed out that for a
given problem of mechanics, there may be many equivalent and unequivalent variational principles. The functional of the so
called generalized variational principles of elasticity with more general forms[16] are linear combinations of the well known functionals given by Reissner and Hu-Washizu. 相似文献
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薛大为 《应用数学和力学(英文版)》1991,12(3):227-236
Two generalized variational principles on nonlinear theory of elasticity with finitedisplacements in which the σ_(ij),e_(i j)and u_i are all three kinds of independent functionsare suggested in this paper.It isproved that these two generalized variational principles areequivalent to each other if the stress-strain relation is satisfied as constraint.Some specialcases,i.e.generalized variational principles on nonlinear theory of elasticity with smalldeformation,on linear theory with finite deformation and on linear theory with smalldeformation together with the corresponding equivalent theorems are also obtained.All ofthem are related to the three kinds of independent variables. 相似文献
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基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础. 相似文献
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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
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An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 相似文献
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薛大为 《应用数学和力学(英文版)》1985,6(6):501-509
A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu ’s generalized variational principle and the Hu’s generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σij, eij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained. 相似文献
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The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang. 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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《International Journal of Solids and Structures》1999,36(34):5177-5206
The generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity, plasticity and unilateral models. The modified forms of the Hu-Washizu and Hellinger-Reissner principles and the displacement-based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables. The related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided. It is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the B-bar method lead to a limitation principle. Accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement⧸pressure variational principle. A second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two-field mixed formulation and the displacement-based method. Numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations, in elasticity or elastoplasticity, under the validity of the limitation principles. 相似文献
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饱和多孔介质耦合系统的几类变分原理 总被引:3,自引:0,他引:3
采用变积方法,建立了一组等温准静态下饱和多孔介质的六类变量的广义变分原理,在此基础上,引入约束条件得到五类变量,四类变量,三类变量和二类变量的变分原理,为建立饱和多孔介质的有限元模型提供了基础。 相似文献