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The thin plate-bending problem is studied. Introducing the stretched variables, the internal layer solutions near the boundary are constructed for the fourth order singularly perturbed boundary problem. Then matching the solutions with outer solution and using the theory of the composite expansion, the asymptotic solution is obtained finally.
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Keywords:
- thin plate bend /
- deflexion /
- asymptotic solution
[1] Alzheimer W E, Davis R T 1968 J. Eng. Mech. Div. Proc. ASCE 4 905
[2] [3] Timoshenk S, Woinowsky-Krieger S 1959 Theory of Plates and Shells McGraw-Hill , Now York.
[4] Besjes J G 1975 J. Math. Appl. 49 24
[5] [6] Mo J Q, Shi B G 1981 Appl. Math. Mech. 2 567
[7] [8] [9] Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys 15 266
[10] [11] Yang Bo, Ding H J, Chen W Q 2008 Appl. Math. Mech. 29 9994
[12] Luminita B, Gheorghe M 2007 Singularly Perturbed Boundary-Value Problem Birkhauser Berlin
[13] [14] [15] Leach J A, Needham D J 2004 Matched Asymptotic Expansions in Reaction-Diffusion Theory,Springer London
[16] Nayfeh A H 1981 Introduction to Perturbation Techniques John Wiley sons New York
[17] [18] [19] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19 030202
[20] [21] Mo J Q 2010 Chin. Phys. B 19 010203
[22] [23] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
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[1] Alzheimer W E, Davis R T 1968 J. Eng. Mech. Div. Proc. ASCE 4 905
[2] [3] Timoshenk S, Woinowsky-Krieger S 1959 Theory of Plates and Shells McGraw-Hill , Now York.
[4] Besjes J G 1975 J. Math. Appl. 49 24
[5] [6] Mo J Q, Shi B G 1981 Appl. Math. Mech. 2 567
[7] [8] [9] Yu D L, Wang G, Liu Y Z, Wen J H, Qiu J 2006 Chin. Phys 15 266
[10] [11] Yang Bo, Ding H J, Chen W Q 2008 Appl. Math. Mech. 29 9994
[12] Luminita B, Gheorghe M 2007 Singularly Perturbed Boundary-Value Problem Birkhauser Berlin
[13] [14] [15] Leach J A, Needham D J 2004 Matched Asymptotic Expansions in Reaction-Diffusion Theory,Springer London
[16] Nayfeh A H 1981 Introduction to Perturbation Techniques John Wiley sons New York
[17] [18] [19] Mo J Q, Lin Y H, Lin W T 2010 Chin. Phys.B 19 030202
[20] [21] Mo J Q 2010 Chin. Phys. B 19 010203
[22] [23] Mo J Q, Chen X F 2010 Chin. Phys. B 19 100203
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