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VARIATIONAL PRINCIPLES OF FLUID FULLFILLED ELASTIC SOLIDS
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作者 石志飞 黄淑萍 章梓茂 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第3期262-268,共7页
The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational pr... The generalized variational principles of isothermal quasi-static fluid full-filled elastic solids are established by using Variational Integral Method. Then by introducing constraints, several kinds of variational principles are worked out, including five-field variable, four-field variable, three-field variable and two-field variable formulations. Some new variational principles are presented besides the principles noted in the previous works. Based on variational principles, finite element models can be set up. 展开更多
关键词 fluid full-filled elastic solids variational integral method variational principles generalized variational principles
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THE VARIATIONAL PRINCIPLES FOR PYROELECTRIC MEDIA 被引量:2
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作者 Wang, XM Shen, YP 《Acta Mechanica Solida Sinica》 SCIE EI 1995年第4期303-313,共11页
The pyroelectric medium is an important material in the application of smart materials and structures. It is necessary to systematically discuss ail kinds of variational principles which play a very significant role i... The pyroelectric medium is an important material in the application of smart materials and structures. It is necessary to systematically discuss ail kinds of variational principles which play a very significant role in the fundamental theory of mechanics and numerical analysis method. This paper firstly gives the quasi-static and the dynamic variational principles,then the principles for eigen problems. As a simple example, the principle was finally applied to derive the fundamental, equations for an anisotropic piezoelectric plate. 展开更多
关键词 continuous mechanics PYROELECTRICITY variational principles smart material
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VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS 被引量:1
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作者 钱伟长 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1984年第3期1281-1296,共16页
In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized var... In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods. 展开更多
关键词 variational principles AND GENERALIZED variational principles IN HYDRODYNAMICS OF VISCOUS FLUIDS
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Equivalent Theorem of Hellinger-Reissner and Hu-Washizu Variational Principles
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作者 何吉欢 《Advances in Manufacturing》 SCIE CAS 1997年第1期36-41,共6页
The paper has proved that Hellinger-Reissuer and Hu-Washizu variational principles are but equivalent principles in elasticity by following three ways: 1) Lagrange multiplier method. The paper points out that only a n... The paper has proved that Hellinger-Reissuer and Hu-Washizu variational principles are but equivalent principles in elasticity by following three ways: 1) Lagrange multiplier method. The paper points out that only a new independent variable can be introduced when one constraint equation has been eliminated by one Lagrange multiplier, which must be expressed as a function of the original variable(s) and/or the new introduced variable after identification. In using Lagrange multiplier method to deduce Hu-Washizu principle from the minimum potential energy principle, which has only one kind of independent variable namely displacement, by eliminating the constraint equations of stress-displacement relations, one can only obtain a principle with two kinds of variables namely displacement and stress; 2) involutory transformation, with such method Hu-Washizu variational principle can be deduce directly from the Hellinger-Reissner variational principle under the same variational constraints of Stress-strain relation, and vice verse; 3)semi-inverse method, by which both of the above variational principles can be deduced from the minimum potential energy principle with tile same variational constraints. So the three kinds of variational functions in Hu-Washizu variational principle are not independent to each other,the stress-strain relationships are still its constraint conditions. 展开更多
关键词 variational principles in elasticity Hellinger-Reissuer variational principle Hu-Washizu variational principle semi-inverse method trial-functional
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Variational principles for two kinds of extended Korteweg-de Vries equations
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作者 曹小群 宋君强 +1 位作者 张卫民 赵军 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第9期59-62,共4页
Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and at... Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct. 展开更多
关键词 He's semi-inverse method variational principles oceanic internal wave atmospheric longwave
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THE RECIPROCAL THEOREM AND LINEAR ELASTIC VARIATIONAL PRINCIPLES
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作者 付宝连 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第3期265-270,共6页
In this paper classical linear elastic variational principles are systematically derivedfrom the reciprocal theorem and mixed variational principles of variations of boundaryconditions are given.
关键词 THE RECIPROCAL THEOREM AND LINEAR ELASTIC variational principles BODY
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USING GENERALIZED VARIATIONAL PRINCIPLES TO RESOLVE THE ST.VENANT’S TORSIONAL BAR WITH A CRACK
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作者 范秀昌 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第2期189-196,共8页
According to generalized variational principles suitable for linear elastic incompatible displacement elements given by Professor Chien Wei-zang, using crack tip singular element and isoparametric surrounding element ... According to generalized variational principles suitable for linear elastic incompatible displacement elements given by Professor Chien Wei-zang, using crack tip singular element and isoparametric surrounding element given by the author of this paper, we will study the St. Venant's torsional bar with a radial vertical crack and compare the present computed results with the results of reference [2], The present computed results show that, using the method provided in this paper, satisfactory convergent solution can be obtained under lower degree of freedom. 展开更多
关键词 USING GENERALIZED variational principles TO RESOLVE THE ST.VENANT S TORSIONAL BAR WITH A CRACK
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A RECTANGULAR ELEMENT OF THIN PLATES BASED UPON THE GENERALIZED VARIATIONAL PRINCIPLES
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作者 钱伟长 王刚 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第11期997-1003,共7页
Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible eleme... Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate. 展开更多
关键词 A RECTANGULAR ELEMENT OF THIN PLATES BASED UPON THE GENERALIZED variational principles
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GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM 被引量:22
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作者 YangXiao 《Acta Mechanica Solida Sinica》 SCIE EI 2005年第1期37-45,共9页
Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical... Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously. 展开更多
关键词 non-local thermal equilibrium thermal-mechanical coupling mathematical model variational principle porous media theory
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Highly accurate symplectic element based on two variational principles 被引量:15
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作者 Guanghui Qing Jia Tian 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第1期151-161,共11页
For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process... For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element(NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses. 展开更多
关键词 Modified H-R mixed variational principle Partial-mixed element Noncompatible symplectic element Finite element method Nearly incompressible material
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GENERALIZED VARIATIONAL PRINCIPLES OF THE VISCOELASTIC BODY WITH VOIDS AND THEIR APPLICATIONS 被引量:2
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作者 盛东发 程昌钧 扶名福 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第4期381-389,共9页
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.... 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. 展开更多
关键词 viscoelastic solid with void variational integral method generalized variational principle generalized potential energy principle Timoshenko beam
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Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory 被引量:1
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作者 徐晓建 邓子辰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第9期1115-1128,共14页
Variational principles for the buckling and vibration of multi-walled carbon nanotubes (MWCNTs) are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary con... Variational principles for the buckling and vibration of multi-walled carbon nanotubes (MWCNTs) are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary conditions coupled by small scale parameters. Hamilton's principle and Rayleigh's quotient for the buckling and vibration of the MWCNTs are given. The Rayleigh-Ritz method is used to study the buckling and vibration of the single-walled carbon nanotubes (SWCNTs) and double-walled carbon nanotubes (DWCNTs) with three typical boundary conditions. The numerical results reveal that the small scale parameter, aspect ratio, and boundary conditions have a profound effect on the buckling and vibration of the SWCNTs and DWCNTs. 展开更多
关键词 variational principle strain gradient theory BUCKLING VIBRATION carbonnanotube
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UNCONVENTIONAL HAMILTON-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF REISSNER SANDWICH PLATE 被引量:1
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作者 黄伟江 罗恩 佘慧 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第1期75-82,共8页
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some uncon ventional Hamilton-type variational principles for dyn... According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo(1987), some uncon ventional Hamilton-type variational principles for dynamics of Reissner sandwich plate can be established systematically. The unconventional Hamilton-type variation principle can fully characterize the initial boundary value problem of this dynamics. In this paper, an important integral relation is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is possible not only to obtain the principle of virtual work in dynamics of Reissner sandwich plate, but also to derive systematically the complementary functionals for fivefield, two-field and one-field unconventional Hamilton-type variational principles by the generalized Legender transformations. Furthermore, with this approach, the intrinsic relationship among the various principles can be explained clearly. 展开更多
关键词 unconventional Hamilton-type variational principle Reissner sandwich plate DYNAMICS dual-complementary relation initial-boundary-value problem
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Generalized variational principles for boundary value problem of electromagnetic field in electrodynamics 被引量:1
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作者 刘彬 王作君 郑世科 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第4期471-480,共10页
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 principl... 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. 展开更多
关键词 generalized variational principle (GVP) electromagnetic field ELECTRODYNAMICS boundary value problem finite element method
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Investigation of power-type variational principles in liquid-filled system 被引量:1
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作者 Haiyan SONG Lifu LIANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第12期1651-1662,共12页
Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clar... Starting from the basic equations of hydrodynamics, the maximum power- type variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic:liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liqUid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures. 展开更多
关键词 HYDRODYNAMICS rigid-body dynamics elasto-dynamics coupling dynamics power-type variational principle
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VARIATIONAL PRINCIPLES OF ASYMMETRIC ELASTICITY THEORY OF FINITE DEFORMATION 被引量:1
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作者 宋彦琦 陈至达 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第11期1200-1206,共7页
In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation ... In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected. 展开更多
关键词 body moment deformation energy finite deformation variation principle
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Hamiltonian Systems in Elasticity and Their Variational Principles 被引量:1
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作者 王治国 唐立民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第2期125-131,共7页
As an inverse problem of Hamiltonian mechanics, a new Hamiltonian system inelasticity and its variational principle are derived from the basic equations of elasticity.
关键词 ELASTICITY Hamiltonian system inverse problem variational principle
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THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY 被引量:1
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作者 付宝连 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1994年第1期37-48,共12页
This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complemen... This paper presents an energy principle, zero different principle of coupledsystems in photoelasticity, from which the potential energy, the complementary energy,generalized potential energy and generalized complementary energy variationalprinciples of the coupled systems in photoelasticity are derived What is called the coupled systems means that two deformational bodies, forwhich figures, sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupledsystems, therefore the above principles become the theoretical basis of defining theinflunce of Poissons ratio v on accuracy of the frozen-stress method. 展开更多
关键词 PHOTOELASTICITY coupled systems zero different work principle coupled variational principle
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Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures
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作者 李纬华 罗恩 黄伟江 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第7期931-942,共12页
According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrica... According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach. 展开更多
关键词 unconventional Hamilton-type variational principle geometric nonlinearity ELASTODYNAMICS orthogonal cable-net structures dual-complementary relation initialboundary-value problem phase space
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STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY
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作者 张国清 余建星 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2004年第3期347-357,共11页
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 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. 展开更多
关键词 ELASTICITY generalized variational principle equivalent theorem scale transformation INVARIANCE
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