A thermomechanical finite element for the analysis of rectangular laminated beams

A new three-noded thermomechanical beam finite element is derived for the analysis of laminated beams. The mechanical part is based on a refined model. The representation of the transverse shear strain by cosine function allows avoiding shear correction factors. This kinematics accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. Concerning the thermal part, a layerwise approach through the thickness is used. Moreover, the continuity of the transverse component of the thermal flux is constrained between the layers. It presents the advantage of reducing the number of temperature unknowns, and improve the results at the interface between two adjacent layers. Mechanical, thermal and thermomechanical tests are presented in order to evaluate the capability of this new finite element to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed.

[1]  T. R. Tauchert,et al.  Thermally Induced Flexure, Buckling, and Vibration of Plates , 1991 .

[2]  Erasmo Carrera,et al.  AN ASSESSMENT OF MIXED AND CLASSICAL THEORIES FOR THE THERMAL STRESS ANALYSIS OF ORTHOTROPIC MULTILAYERED PLATES , 2000 .

[3]  E. Carrera,et al.  CLOSED-FORM SOLUTIONS TO ASSESS MULTILAYERED-PLATE THEORIES FOR VARIOUS THERMAL STRESS PROBLEMS , 2004 .

[4]  Maurice Touratier,et al.  A refined theory of laminated shallow shells , 1992 .

[5]  J. N. Reddy,et al.  A generalization of two-dimensional theories of laminated composite plates† , 1987 .

[6]  Olivier Polit,et al.  AC1 finite element including transverse shear and torsion warping for rectangular sandwich beams , 1999 .

[7]  T. K. Varadan,et al.  A new theory for accurate thermal/mechanical flexural analysis of symmetric laminated plates , 1999 .

[8]  H. Murakami,et al.  TRANSIENT THERMAL STRESS ANALYSIS OF A LAMINATED COMPOSITE BEAM , 1989 .

[9]  M. Touratier,et al.  A rectangular finite element for analysing composite multilayered shallow shells in statics, vibration and buckling , 1993 .

[10]  Santosh Kapuria,et al.  AN EFFICIENT HIGHER-ORDER ZIGZAG THEORY FOR LAMINATED PLATES SUBJECTED TO THERMAL LOADING , 2004 .

[11]  M. Touratier,et al.  An efficient standard plate theory , 1991 .

[12]  Olivier Polit,et al.  A new eight‐node quadrilateral shear‐bending plate finite element , 1994 .

[13]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[14]  Maurice Touratier,et al.  A generalization of shear deformation theories for axisymmetric multilayered shells , 1992 .

[15]  M. Touratier,et al.  A constrained discrete layer model for heat conduction in laminated composites , 2005 .

[16]  T. K. Varadan,et al.  THERMOELASTIC SOLUTIONS FOR ORTHOTROPIC AND ANISOTROPIC COMPOSITE LAMINATES , 1996 .

[17]  Santosh Kapuria,et al.  An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading , 2003 .

[18]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[19]  Ahmed K. Noor,et al.  Computational Models for High-Temperature Multilayered Composite Plates and Shells , 1992 .