CONSIDER SAINT-VENANT''''S PRINCIPLE BY MEANS OF CHAIN MODEL

ＩｎｔｒｏｄｕｃｔｉｏｎＡｃｃｏｒｄｉｎｇｔｏＬｏｖｅ[1],Ｓａｉｎｔ＿Ｖｅｎａｎｔ’ｓＰｒｉｎｃｉｐｌｅｃａｎｂｅｅｘｐｒｅｓｓｅｄａｓ:Ｔｈｅｅｆｆｅｃｔｏｆａｓｅｌｆ-ｅｑｕｉｌｉｂｒａｔｅｄｓｙｓｔｅｍｏｆｆｏｒｃｅｓａｃｔｉｎｇｉｎａｓｐｈｅｒｅｗｉｌｌｒｅｓｔｒｉｃｔｉｎａｓｍａｌｌｄｏｍａｉｎｎｅａｒｔｈｅｓｐｈｅｒｅ .Ｔｈｉｓｐｒｉｎｃｉｐｌｅｉｓｔｈｅｂｒｉｄｇｅｂｅｔｗｅｅｎｔｈｅｅｌａｓｔｉｃｉｔｙｔｈｅｏｒｙａｎｄａｐｐｌｉｃａｔｉｏｎ ,ｂｕｔｉｔｈａｓｎｏｔｂｅｅｎｐｒｏｖ…     

THE CONSERVATION LAW OF NONHOLONOMIC SYSTEM OF SECOND-ORDER NON-CHETAVE''''S TYPE IN EVENT SPACE

ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｎｏｔｏｎｌｙｈａｓｉｍｐｏｒｔａｎｃｅｉｎｍａｔｈｅｍａｔｉｃｓｂｕｔａｌｓｏｒｅｖｅａｌｓｐｒｏｆｏｕｎｄｐｈｙｓｉｃａｌｌａｗ .Ｉｎ 1 91 8,ｂａｓｅｄｏｎｉｎｖａｒｉａｎｃｅｏｆＨａｍｉｌｔｏｎ’ｓｐｒｉｎｃｉｐｌｅｕｎｄｅｒｉｎｆｉｎｉｔｅｓｉｍａｌｔｒａｎｓｆｏｒｍａｔｉｏｎ ,ｔｈｅｃｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃｓｓｙｓｔｅｍｗａｓｓｔｕｄｉｅｄｂｙＧｅｒｍａｎｓｃｉｅｎｔｉｓ…     

VARIATIONAL METHOD AND COMPUTATION FOR H_∞ CONTROL

ＩｎｔｒｏｄｕｃｔｉｏｎＨ∞ｃｏｎｔｒｏｌｔｈｅｏｒｙｈａｓｂｅｅｎｗｅｌｌｄｅｖｅｌｏｐｅｄｓｉｎｃｅｔｈｅＤＧＫＦｐａｐｅｒ[1],ｗｈｅｒｅｔｈｅｆｕｎｄａｍｅｎｔａｌｅｑｕａｔｉｏｎｓｆｏｒＨ∞ ｍｅａｓｕｒｅｍｅｎｔｆｅｅｄｂａｃｋｃｏｎｔｒｏｌａｒｅｄｅｒｉｖｅｄｆｒｏｍｔｈｅｓｅｐａｒａｔｉｏｎｐｒｉｎｃｉｐｌｅ ,ａｓｉｎＬＱＧｃｏｎｔｒｏｌｔｈｅｏｒｙ[2～ 5 ].Ｈｏｗｅｖｅｒ,ｔｈｅｃｏｍｐｕｔａｔｉｏｎｆｏｒｆｉｎｉｔｅｈｏｒｉｚｏｎ [0 ,ｔｆ]ｐｒｏｂｌｅｍａｎｄｔｈｅｄｅｔｅｒｍｉ…     

D'alembert principle in the velocity space

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｒｅｓｅａｒｃｈｅｒｓｈａｖｅｂｅｅｎｍａｄｅｏｎｔｈｅｖａｒｉｏｕｓｆｏｒｍｕｌａｅｏｆＤ’Ａｌｅｍｂｅｒｔｐｒｉｎｃｉｐｌｅ,ａｔｔｅｎｔｉｏｎｈａｓｂｅｅｎｇｉｖｅｎｔｏｍｅｃｈａｎｉｃａｌｐｒｉｎｃｉｐｌｅｓｉｎｔｈｅｖｅｌｏｃｉｔｙｓｐａｃｅａｎｄｔｈｅｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｉｎｔｈｅｖｅｌｏｃｉｔｙｓｐａｃｅ,ａｎｄｔｈｅｖｅｌｏｃｉｔｙｓｐａｃｅｏｆｒｅｌａｔｉｖｉｓｔｉｃｍｅｃｈａｎｉｃｓｈａｓｂｅｅｎｍａｄｅ…     

A Universal Variational Formulation for Two Dimensional Fluid Mechanics

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 50’ｓ,ｇｒｅａｔｐｒｏｇｒｅｓｓｈａｄｂｅｅｎｍａｄｅｏｎｔｈｅｒｅｓｅａｒｃｈｏｆｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｉｎｓｏｌｉｄｍｅｃｈａｎｉｃｓｗｉｔｈＨｕ＿Ｗａｓｈｉｚｕｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅ(ＧＶＰ) [1]ａｓｍｉｌｅｓｔｏｎｅ ,ａｎｄｉｎｆｌｕｉｄｍｅｃｈａｎｉｃｓｗｉｔｈＣ .Ｃ .Ｌｉｎ’ｓｃｏｎｓｔｒａｉｎｓ[2 ]ａｓｍｉｌｅｓｔｏｎｅ .Ｉｎ 80’ｓ,ＣｈｉｅｎＷｅｉ＿ｚａｎｇｄｅｄｕｃｅｄａｍｏｒｅｇｅｎｅｒａｌ…     

SERIES PERTURBATIONS APPROXIMATE SOLUTIONS TO N-S EQUATIONS AND MODIFICATION TO ASYMPTOTIC EXPANSION MATCHED METHOD

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅａｓｙｍｐｔｏｔｉｃｅｘｐａｎｓｉｏｎｍａｔｃｈｅｄｍｅｔｈｏｄｗａｓｄｅｖｅｌｏｐｅｄｏｎｔｈｅｂａｓｉｓｏｆＰｌａｎｄｔｌ’ｓＢｏｕｎｄａｒｙＬａｙｅｒｓＴｈｅｏｒｙ[1- 3].Ｉｎ 1 960’ｓｌａｔｅｒ,ｔｈｅｖａｌｉｄｍａｔｃｈｅｄｐｒｉｎｃｉｐｌｅｓｗｅｒｅａｄｖａｎｃｅｄｂｙＶａｎＤｙｋｅａｎｄＫａｐｌｕｎ[4 ,5 ],ｒｅｓｐｅｃｔｉｖｅｌｙ .Ｂｕｔｔｈｅａｐｐｌｉｃａｂｌｅｒａｎｇｅｏｆｔｈｅｍｅｔｈｏｄｗａｓｒｅｓｔｒｉｃｔｅｄｂｙｔｈｅｄｉｆｆｉｃｕｌｔｙｔｈ…     

Axisymmetric bending for thick laminated circular plate under a concentrated load

Ｎｏｗａｄａｙｓ,ｔｈｅｃｕｒｒｅｎｔｔｈｅｏｒｉｅｓｏｆｐｌａｔｅｓａｎｄｓｈｅｌｌｓ,ｓｕｃｈａｓＫｉｒｃｈｈｏｆｆ’ｓｔｈｉｎｐｌａｔｅｔｈｅｏｒｙａｎｄＲｅｉｓｓｎｅｒ’ｓｍｏｄｅｒａｔｅｌｙｔｈｉｃｋｐｌａｔｅｔｈｅｏｒｙｅｔｃ．,ａｒｅｅ...     

Solution of the Rayleigh problem for a powerlaw non-Newtonian conducting fluid via group method

ＩｎｔｒｏｄｕｃｔｉｏｎＦｌｕｉｄｓｔｈａｔｏｂｅｙＮｅｗｔｏｎ’ｓｌａｗｏｆｖｉｓｃｏｓｉｔｙａｒｅｃａｌｌｅｄＮｅｗｔｏｎｉａｎｆｌｕｉｄｓ.Ｎｅｗｔｏｎ’ｓｌａｗｏｆｖｉｓｃｏｓｉｔｙｉｓτ=μｄｕ/ｄｔ,ｗｈｅｒｅτｉｓｔｈｅｓｈｅａｒｓｔｒｅｓｓａｎｄμｉｓｔｈｅｖｉｓｃｏｓｉｔｙ .ＮｏｔａｌｌｆｌｕｉｄｓｆｏｌｌｏｗｔｈｅＮｅｗｔｏｎｉａｎｓｔｒｅｓｓ＿ｓｔｒａｉｎｒｅｌａｔｉｏｎ .Ｓｏｍｅｆｌｕｉｄｓ ,ｓｕｃｈａｓｋｅｔｃｈｕｐ ,ａｒｅｓｈｅａｒｔｈｉｎｎｉｎｇ ,ｔｈａｔｉｓ,ｔｈｅｃ…     

DYNAMICS IN NEWTONIAN-RIEMANNIAN SPACE-TIME (Ⅱ)

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ (Ⅰ ) (ｓｅｅ:ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓａｎｄＭｅｃｈａｎｉｃｓ (ＥｎｇｌｉｓｈＥｄｉｔｉｏｎ) ,2 0 0 0 ,2 1 (7) :82 5-83 5) ,ｗｅｈａｖｅｅｓｔａｂｌｉｓｈｅｄｔｈｅｄｙｎａｍｉｃｓｉｎＮｅｗｔｏｎｉａｎ＿Ｒｉｅｍａｎｎｉａｎｓｐａｃｅ＿ｔｉｍｅ,ａｎｄｇｉｖｅｉｔｓａｐｐｌｉｃａｔｉｏｎｔｏＨｙｄｒｏｍｅｃｈａｎｉｃｓ.ＴｈｅｒｅｉｓＧａｌｉｌｅｏ’ｓｐｒｉｎｃｉｐｌｅｏｆｒｅｌａｔｉｖｉｔｙｉｎＣｌａｓｓｉｃａｌＮｅｗｔｏｎ’ｓｍｅｃｈａ…     

GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 996,Ｋｈａｍｓｉ[1]ｅｓｔａｂｌｉｓｈｅｄｔｈｅｈｙｐｅｒｃｏｎｖｅｘｖｅｒｓｉｏｎｏｆｔｈｅｆａｍｏｕｓＦａｎ＿ＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅ .Ｙｕａｎ[2 ,3]ｏｂｔａｉｎｓｏｍｅｃｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆＫＫＭｐｒｉｎｃｉｐｌｅｉｎｈｙｐｅｒｃｏｎｖｅｘｓｐａｃｅｓ,ａｎｄａｓａｐｐｌｉｃａｔｉｏｎｓｏｆｔｈｅｉｒｒｅｓｕｌｔｓ,ｓｏｍｅｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｓａｎｄｍａｔｃｈｉｎｇｔｈｅｏｒｅｍｓｆｏｒｏｐｅｎａ…     

Semi-inverse method and generalized variational principles with multi-variables in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ 1 954,Ｈｕ[1,2 ]ｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅｂｙｓｏ＿ｃａｌｌｅｄｔｒｉａｌ＿ａｎｄ＿ｅｒｒｏｒｍｅｔｈｏｄ ,ａｎｄｉｎ1 964 ,Ｃｈｉｅｎ[3]ｓｙｓｔｅｍａｔｉｃａｌｌｙｄｉｓｃｕｓｓｅｄｔｈｅＬａｇｒａｎｇｅｍｕｌｔｉｐｌｉｅｒｍｅｔｈｏｄ ,ｂｙｗｈｉｃｈｈｅｓｕｃｃｅｓｓｆｕｌｌｙｄｅｄｕｃｅｄＨｕ＿Ｗａｓｈｉｚｕｐｒｉｎｃｉｐｌｅ.Ａｆｔｅｒｔｈａｔｇｅｎｅｒａｌｉｚｅｄｖａｒｉａｔｉｏｎａｌｐｒｉｎｃｉｐｌｅｓｃａｎｂｅａｒｒｉｖｅｄａｔ…     

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

ＩｎｔｒｏｄｕｃｔｉｏｎＡｍａｊｏｒｐｒｏｂｌｅｍｏｆｏｎｅｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃｓｉｓｔｏｓｔｕｄｙｔｈｅａｔｔｒａｃｔｏｒｓｏｆｉｎｔｅｒｖａｌｍａｐｓ,ｉ.ｅ.ｔｈｅｃｌａｓｓｉｆｉｃａｔｉｏｎａｎｄｓｔｒｕｃｔｕｒｅｏｆａｔｔｒａｃｔｏｒｓ.ＦｏｌｌｏｗｉｎｇＭｉｌｎｏｒ’ｓｄｅｆｉｎｉｔｉｏｎｏｎａｔｔｒａｃｔｏｒｓ[1],ｉｆｆｉｓａｕｎｉｍｏｄａｌｍａｐｗｉｔｈｎｅｇａｔｉｖｅＳｃｈｗａｒｚｉａｎｄｅｒｉｖａｔｉｖｅ ,ｔｈｅｎｂｙＧｕｃｋｅｎｈｅｉｍｅｒ’ｓｔｈｅｏｒｅｍ[2 ]…     

New studying of Lattice Boltzmann method for two-phase driven in porous media

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｔｗｏ＿ｐｈａｓｅｄｒｉｖｅｎｉｎｐｏｒｏｕｓｍｅｄｉａｉｓａｎｉｍｐｏｒｔａｎｔｓｕｂｊｅｃｔｏｆｗｉｄｅｉｎｔｅｒｄｉｓｃｉｐｌｉｎａｒｙｃｏｎｃｅｒｎ ,ｓｕｃｈａｓｐｅｔｒｏｌｅｕｍｉｎｄｕｓｔｒｙ ,ｓｕｂｔｅｒｒａｎｅａｎ ,ｃｈｅｍｉｃａｌｐｒｏｊｅｃｔｅｔｃ..Ｉｔ’ｓｖｅｒｙｄｉｆｆｉｃｕｌｔｉｆｗｅａｄｏｐｔｎｕｍｅｒｉｃａｌｉｎｔｅｇｒａｌｍｅｔｈｏｄｆｏｒｔｈｅｃａｓｅｏｆｍｕｌｔｉｐｈａｓｅａｎｄｍｕｌｔｉｃｏｍｐｏｓｉｔｉｏｎ ,ｔｈｅｃｒｕｘｏｆ…     

Subharmonic and ultra-subharmonic response of nonlinear elastic beams subjected to harmonic excitation

Ｔｈｅｄｙｎａｍｉｃｒｅｓｐｏｎｓｅｐｒｏｂｌｅｍｓｏｆｅｌａｓｔｉｃｓｔｒｕｃｔｕｒｅｈｏｌｄｍｏｒｅａｎｄｍｏｒｅｉｎｔｅｒｅｓｔ．Ｉｎｔｈｅｅａｒｌｙ１９７０’ｓ．Ｗ．Ｙ．Ｔｓｅｎｇｅｔａｌ．［１,２］ｉｎｖｅｓｔｉｇａｔｅｄｆｉｘｅｄ＿ｅｎｄｅｄｂｅａｍｓ．Ｆｉｒｓｔ,ｔｈｅｓｉｎｇｌｅｍｏｄｅａｎｄｔｗｏｍｏｄｅｓｗｅｒｅｕｓｅｄｔｏｔｒａｎｓｆｏｒｍｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｃｏｎｔｒｏｌｌｉｎｇｅｑｕａｔｉｏｎｓｉｎｔｏｏｒｄｉｎａｌｄｉｆｆｅｒｅｎｔｉａｌｄｙｎａｍｉ…     

Minimal essential sets and essential components of the equilibria of production economies

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ [1 ] ,Ｄｉｅｒｋｅｒｉｎｔｒｏｄｕｃｅｄｔｈｅｃｏｎｃｅｐｔｏｆｅｓｓｅｎｔｉａｌｅｑｕｉｌｉｂｒｉａｆｏｒｐｕｒｅｅｘｃｈａｎｇｅｅｃｏｎｏｍｉｅｓａｎｄｐｒｏｖｅｄｔｈａｔｉｎ‘ｍｏｓｔ’ｐｕｒｅｅｘｃｈａｎｇｅｅｃｏｎｏｍｉｅｓ (ｉｎｔｈｅｓｅｎｓｅｏｆＢａｉｒｅｃａｔｅｇｏｒｙ)ａｌｌｅｑｕｉｌｉｂｒｉａａｒｅｅｓｓｅｎｔｉａｌ.Ｉｎ [2 ] ,ｔｈｅｃｏｎｃｅｐｔｏｆｅｓｓｅｎｔｉａｌｅｑｕｉｌｉｂｒｉａｆｏｒｐｒｏｄｕｃｔｉｏｎｅｃｏｎｏｍｉｅｓｗａｓｆｉｒｓｔ…     

Anomalous dynamics response of nonlinear elastic bar

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｓｅｎｔｙｅａｒｓ,ｔｈｅｃｈａｏｔｉｃｂｅｈａｖｉｏｒｏｆｂｅａｍｓｓｕｂｊｅｃｔｅｄｔｏｐｅｒｉｏｄｉｃｌｏａｄｂｒｉｎｇｓｍｏｒｅａｎｄｍｏｒｅｓｃｈｏｌａｒｓ’ｉｎｔｅｒｅｓｔｓ.Ｉｎ 1 983 ,ＦＣＭｏｏｎｅｔａｌ.[1]ｓｔｕｄｉｅｄｔｈｅｃｈａｏｔｉｃｍｏｔｉｏｎｓｏｆｂｅａｍｓｉｎｎｏｎｌｉｎｅａｒｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ.Ｉｎ 1 994 ,Ｓ .ＡｎａｎｔｈａＲａｍｕａｎｄＴＳＳａｎｋａｒｅｔａｌ.[2 ]ａｎａｌｙｚｅｄｂｉｆｕｒｃａｔｉｏｎａｎｄＣａｔａ…     

New Principles of Work and Energy as Well as Power and Energy Rate for Continuum Field Theories

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A discrete algorithm for complex frequency-domain convolutions

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