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Applied Mathematics and Mechanics(English Edition) 2000年第3期21卷 327-334页

作者：虞爱民 Key Laboratory of Solid Mechanics of MOE Tongji University Shanghai P R China

Naturally curved and twisted closed thin-walled slender beams of composite material undergoing small strains, large displacements and rotations have been investigated, and an incomplete generalized variational function on theory of elasticity with finite displacement is established far these beams with complete constrained boundaries at two ends. The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition. The above-mentioned method can also be extended to other various incomplete constrained boundaries conveniently. In addition, the fundamental equations and concerned formulas in the small displacement theory of the beams can be derived by using above results.

关键词： generalized variational principle geometric nonlinear finite displacement

generalized variational principleS OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS

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Applied Mathematics and Mechanics(English Edition) 2004年第4期25卷 381-389页

作者：盛东发程昌钧扶名福 Shanghai Institute of Applied Mathematics and Mechanics Department of Mechanics Shanghai University Graduate School of Engineering Mechanics Institute of Civil Engineering Nanchang University

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 the initial 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.

关键词： viscoelastic solid with void variational integral method generalized variational principle generalized potential energy principle Timoshenko beam

REGION-WISE variational principleS AND generalized variational principleS ON LARGE STRAIN FOR CONSOLIDATION THEORY

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Applied Mathematics and Mechanics(English Edition) 2005年第7期26卷 944-952页

作者：罗晓辉李永乐罗昕 School of Civil Engineering Huazhong University of Science & Technology Wuhan 430074 P.R.China Department of Geotechnique Huabei Hydraulic and Hydroelectric Engineering Institute Zhengzhou 450008 P.R.China

The difference of constitutive character and large deformation as to soil mass are basic questions to analyze deformational feature. According to the description method of limited deformation, the large deformation consolidation equations of soil mass were created and its variational principles were rigorously testified. The regionwise variational principles of consolidation theory were deduced using sub-structure continuous condition of region-wise. Quoting the method of Lagrangian multiplier operator, generalized variational principles of region-wise of large deformation consolidation in the nonconstrained condition were created and approved.

关键词： large strain consolidation variational principle region-wise variation generalized variational principle

STUDY OF THE EQUIVALENT THEOREM OF generalized variational principleS IN ELASTICITY

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Applied Mathematics and Mechanics(English Edition) 2004年第3期25卷 347-357页

作者：张国清余建星 Civil Engineering College Tianjin University

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.

关键词： elasticity generalized variational principle equivalent theorem scale transformation invariance

THE　MATHEMATICAL　MODELS　AND　generalized　variational　principleS　OF　NONLINEAR　ANALYSIS　FOR　PERFORATED　THIN　PLATES

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Applied Mathematics and Mechanics(English Edition) 1996年第2期17卷 109-118页

作者：程昌钧杨骁 Department of Mechanics Lanzhou University Lanzhou Gansu P. R. China

On foe basis of the Kirchoff-Karman hypothses for the nonlinear bending of thin plates, the three kinds of boundary value problems of nonlinear analysis for perforated fhin plates are presented under the differenr in-plane boundary conditions and the corresponding generalized varialional principles are established. One can see that all mathematical models presented in this paper are completely new ones and differ from the ordinary von Karman theory. These mathematical models can be applied to the nonlinear analysis and the Stability analysis of perforaled thin plates in arbitraryplane boundary conditions.

关键词： perforated thin plate non-linear analysis mathematical model generalized variational principle

THE APPLICATIONS OF generalized variational principleS IN NONLINEAR STRUCTURAL ANALYSIS

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Applied Mathematics and Mechanics(English Edition) 1993年第5期14卷 417-428页

作者：成祥生 Tongji University Shanghai

This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.

关键词： generalized variational principle nonlinear structures statically indeterminate structures

The generalized quasi-variational principles of non-conservative systems with two kinds of variables

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Science China(Physics,Mechanics & Astronomy) 2005年第5期 90-103页

作者： LIANG Lifu, LIU Diankui & SONG Haiyan School of Civil Engineering, Harbin Engineering University, Harbin 150001, China

According to the corresponding relations between general forces and general displacements, the balancing and geometrical equations of elasticity are multiplied by the corresponding virtual quantities, integrated with volume and area, and then added algebraically. Proceeding to the next step, by substituting constitutive relation and considering that body force and surface force are both fellow forces, the generalized quasi-variational principles with the two kinds of variables of the first type are established in non-conservative systems. Through substituting another constitutive relation, using similar methods as above, the generalized quasi-variational principles with the two kinds of variables of the second type are established in non-conservative systems. By using the generalized quasi-complementary energy principles with the two kinds of variables of the first type, a method for solving two kinds of variables (internal force and deformation) is given for non-conservative systems of the typical fellow forces.

关键词： non-conservative system generalized variational principle two kinds of variables.

generalized mixed finite element method for 3D elasticity problems

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Acta Mechanica Sinica 2018年第2期34卷 371-380页

作者： Guanghui Qing Junhui Mao Yanhong Liu College of Aeronautical Engineering Civil Aviation University of China

Without applying any stable element techniques in the mixed methods, two simple generalized mixed element(GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner(H–R) variational principle. The main features of the GME formulations are that the common C0-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.

关键词： Minimum potential energy principle Hellinger–Reissner (H–R) variational principle generalized variational principle generalized mixed element (GME) Elasticity problem Noncompatible mode

THE FIRST-ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARYUNDER UNIFORM SURFACE LOADING (Ⅱ)

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Applied Mathematics and Mechanics(English Edition) 1997年第5期18卷 103-112页

作者：钱伟长 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai P. R. China

Based upon Ihe differntial equations and their related boundary conditions givenin the prerious papert[1], this poper finds the analytical solution of non-Kirchhoff-Lovetheory for elastic circular plate with fixed boundary conditions under uniform surfaceloading. However, for the sake of Saving conrputational work. the first orderapproximation theory can be further simplified in more rational bases.

关键词： elastieity circular plate Kirchhoff-Love assumptions generalized variational principle

Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction

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Applied Mathematics and Mechanics(English Edition) 2008年第8期29卷 1023-1032页

作者：王省哲 Key Laboratory of Mechanics on Western Disasters and Environment Lanzhou University Lanzhou 730000P.R.China

Based on the magnetoelastic generalized variational principle and Hamilton＇s principle, a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed in this paper. From the variational manipulation of magnetic scale potential and elastic displacement, all the fundamental equations for the magnetic field and mechanical deformation, as well as the magnetic body force and magnetic traction for describing magnetoelastic interaction are derived. The theoretical model is applied to a ferromagnetic rod vibrating in an applied magnetic field using a perturbation technique and the Galerkin method. The results show that the magnetic field will change the natural frequencies of the ferromagnetic rod by causing a decrease with the bending motion along the applied magnetic field where the magnetoelastic buckling will take place, and by causing an increase when the bending motion of the rod is perpendicular to the field. The prediction by the mode presented in this paper qualitatively agrees with the natural frequency changes of the ferromagnetic rod observed in the experiment.

关键词： ferromagnetic rod magnetoelastic interaction generalized variational principle vibration frequency perturbation method