TY - JOUR
T1 - Asymptotic thermoelastic analysis of anisotropic inhomogeneous and laminated plates
AU - Tarn, Jiann Quo
AU - Wang, Yung Ming
N1 - Funding Information:
Received 9 September 1993. This work is supported by the National Science Council of R.O.C. through Grant NSC83-0410-E-006-040. Address correspondence to Jiann-Quo Tam, Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, Republic of China.
PY - 1995
Y1 - 1995
N2 - On the basis of three-dimensional elasticity without a priori assumptions, we develop an asymptotic theory for the thermoelastic analysis of anisotropic inhomogeneous plates subject to general temperature variations and under the action of lateral loads. The inhomogeneities considered are in the thickness direction, and the laminated plate represents an important special case. Through reformulation of the basic equations and nondimensionalization of the field variables, we find that the method of asymptotic expansions is well suited for the problem. Upon using the asymptotic expansion, we obtain sets of recurrence equations that can be integrated successively to determine the solution for a problem. We show that the classical laminated plate theory (CLT) is merely the leading-order approximation in the asymptotic theory. Furthermore, the higher-order equations are essentially the same as the CLT equations, only with nonhomogeneous terms that are completely determined from the lower-order solutions. As a result, the three-dimensional asymptotic solution for a thermoelasticity problem of the laminated plate can be obtained in a systematic way no more difficult than the CLT. The theory is illustrated by considering an inhomogeneous plate subject to a temperature variation and a laminated plate subject to a general thermomechanical loading.
AB - On the basis of three-dimensional elasticity without a priori assumptions, we develop an asymptotic theory for the thermoelastic analysis of anisotropic inhomogeneous plates subject to general temperature variations and under the action of lateral loads. The inhomogeneities considered are in the thickness direction, and the laminated plate represents an important special case. Through reformulation of the basic equations and nondimensionalization of the field variables, we find that the method of asymptotic expansions is well suited for the problem. Upon using the asymptotic expansion, we obtain sets of recurrence equations that can be integrated successively to determine the solution for a problem. We show that the classical laminated plate theory (CLT) is merely the leading-order approximation in the asymptotic theory. Furthermore, the higher-order equations are essentially the same as the CLT equations, only with nonhomogeneous terms that are completely determined from the lower-order solutions. As a result, the three-dimensional asymptotic solution for a thermoelasticity problem of the laminated plate can be obtained in a systematic way no more difficult than the CLT. The theory is illustrated by considering an inhomogeneous plate subject to a temperature variation and a laminated plate subject to a general thermomechanical loading.
UR - http://www.scopus.com/inward/record.url?scp=0029203899&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0029203899&partnerID=8YFLogxK
U2 - 10.1080/01495739508946289
DO - 10.1080/01495739508946289
M3 - Article
AN - SCOPUS:0029203899
SN - 0149-5739
VL - 18
SP - 35
EP - 58
JO - Journal of Thermal Stresses
JF - Journal of Thermal Stresses
IS - 1
ER -