ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (9): 997-1008.

• 论文 • 下一篇

ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

何陵辉¹, 林志华², 刘人怀³

1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, P. R. China;
2. Department of Building and Construction, City University of Hong Kong, Hong Kong, P. R. China;
3. Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P. R. China

收稿日期:2002-02-04 修回日期:2003-04-22 出版日期:2003-09-18 发布日期:2003-09-18
基金资助:
the National Natural Science Foundation of China (10272069);the Shanghai Key Subject Program

ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

HE Ling-hui¹, LIM Chee-wah², LIU Ren-huai ³

1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, P. R. China;
2. Department of Building and Construction, City University of Hong Kong, Hong Kong, P. R. China;
3. Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P. R. China

Received:2002-02-04 Revised:2003-04-22 Online:2003-09-18 Published:2003-09-18
Supported by:
the National Natural Science Foundation of China (10272069);the Shanghai Key Subject Program

摘要/Abstract

摘要： Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state-space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid-plane, which are governed by a set of two-dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two-dimensional equations immediately gives the three-dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.

Abstract: Elastic layers with varying dilative eigenstrains through the thickness were concerned. A general procedure was proposed for the analysis of such layers under arbitrary loads. The study is based on the state-space method and an asymptotic expansion technique. When the external loads are uniform, the expansion terminates after some leading terms, and an explicit representation for the mechanical field in a layer is obtained. This representation relies only on the displacement components of the mid-plane, which are governed by a set of two-dimensional differential equations similar to those in the classical plate theory. Consequently, obtaining the solution to the two-dimensional equations immediately gives the three-dimensional responses of the layer. As an illustrative example, a clamped elliptical layer under a uniformly distributed transverse load is analyzed in detail.

中图分类号:

O781
74B20

何陵辉;林志华;刘人怀. ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 997-1008.

HE Ling-hui;LIM Chee-wah;LIU Ren-huai . ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 997-1008.

参考文献

[1] Green D J, Tandon R, Sglavo V M. Crack arrest and multiple cracking in glass through the use of designed residual stress profiles [J]. Science, 1999, 283 (5406):1295-1297.
[2] Chan H M. Layered ceramics:processing and mechanical behavior[J]. Ann Rev Mat Sci, 1997, 27:249-282.
[3] Yoo J, Cho K, Bae W S, et al. Transformation-toughened ceramic multilayers with compositional gradients[J]. J Am Ceran Soc, 1998, 81(1):21-32.
[4] Noor A K, Burton W S. Assessment of shear deformation theories for multilayered composite plates[J]. Appl Mech Rev, 1989, 42(1):1-13.
[5] Kaprielian P V, Rogers T G, Spencer A J M. Exact theory for the stretching and the bending of laminated plates by edge loading- Ⅰ:Isotropic plates[J]. Phil Trans Roy Soc London, 1988, A234(2):565-594.
[6] Rogers T G, Waston P, Spencer A J M. An exact three-dimensional solution for normal loading of inhomogeneous and laminated anisotropic elastic plates of moderate thickness [J]. Proc Roy Soc London, 1992, A437(1):199-213.
[7] Freund L B. The stress distribution and curvature of a general compositionally graded semiconductor layer[J]. J Cryst Growth, 1993, 132(1/2):341-344.
[8] Freund L B. Some elementary connections between curvature and mismatch strain in compositionally graded thin films[J]. J Mech Phys Solids, 1996, 44(5):723-736.
[9] Lee J S, Jiang L Z. Exact electroelastic analysis of piezoelectric laminae via state space approach[J]. Int J Solids Struct, 1996, 33(7):977-990.
[10] Cheng Z Q, Lim C W, Kitipomchai S. Three-dimensional exact solution for inhomogeneous and laminated piezoelectric plates[J]. Int J Engng Sci, 1999, 37(11), 1425-1439.
[11] HE Ling-hui. Axisymmetric response of circular plates with piezoelectric layers:an exact solution[J]. Int J Mech Eng, 1998, 40(12):1265-1279.
[12] HE Ling-hui. Three-dimensional analysis of some symmetric hybrid piezoelectric laminates[J]. Z Angew Math Mech, 2000, 80(5):307-318.
[13] HE Ling-hui, Lim C W, Soh A K. Three-dimensional analysis of an antiparalell piezoelectric bimorph[J]. Acta Mech, 2000, 145(1-4):189-204.
[14] Lim C W, HE Ling-hui, Soh A K. Three-dimensional electromechanical responses of a parallel piezoelectric bimorph[J]. Int J Solids Struct, 2001, 38(16):2833 -2849.
[15] Timoshenko S P, Woinowsky-Krieger S. Theory of Plates and Shells [M]. New York:McGrawHill, 1959.
[16] Gantmacher F R. The Theory of Matrix[M]. New York:Chelsea, 1960.

ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

ANALYSIS OF ELASTIC LAYERS WITH DILATIVE EIGENSTRAINS VARYING THROUGH THE THICKNESS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价