TY - JOUR

T1 - Efficient linear transverse normal stress analysis of layered composite plates

AU - Rolfes, R.

AU - Rohwer, K.

AU - Ballerstaedt, M.

N1 - Funding information: The contribution of Mr Valter Carvelli from the University of Bologna who provided the three-dimensional solutions for the antisymmetric laminate is gratefully acknowledged. His stay at the DLR was supported through the EU program Human Capital and Mobility under the contract no. CHRX-CT93-0383, Mechanics of Composite Materials and Structures.

PY - 1999/2/23

Y1 - 1999/2/23

N2 - Based on the first order shear deformation theory (FSDT) a method is developed for calculating the transverse normal stress (in thickness direction) in layered composite plate structures. Two steps are necessary. First, the transverse shear stress calculation, and second, relying on the results of the first step, the transverse normal stress evaluation. In the first step strain derivatives are substituted with transverse shear forces which in turn are obtained from the corresponding material law. This leads to a derivative-free process which is numerically more accurate than a pure equilibrium approach. As a second step the transverse normal stress is equilibrated to the derivatives of the transverse shear stresses with respect to the in-plane coordinates. As compared to the standard equilibrium approach, the proposed procedure reduces the order of differentiation by one. Thus, only quadratic shape functions are necessary for evaluating the required derivatives on the element level. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show that the exact three-dimensional elasticity solution is very closely approximated. This holds for thin as well as rather thick plates with a slenderness ratio down to five. In contrast to many recently established methods, either higher order lamination theories or layerwise theories, the approach is easily applicable to finite elements, since only C0-continuity is necessary and the numerical effort is low.

AB - Based on the first order shear deformation theory (FSDT) a method is developed for calculating the transverse normal stress (in thickness direction) in layered composite plate structures. Two steps are necessary. First, the transverse shear stress calculation, and second, relying on the results of the first step, the transverse normal stress evaluation. In the first step strain derivatives are substituted with transverse shear forces which in turn are obtained from the corresponding material law. This leads to a derivative-free process which is numerically more accurate than a pure equilibrium approach. As a second step the transverse normal stress is equilibrated to the derivatives of the transverse shear stresses with respect to the in-plane coordinates. As compared to the standard equilibrium approach, the proposed procedure reduces the order of differentiation by one. Thus, only quadratic shape functions are necessary for evaluating the required derivatives on the element level. Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show that the exact three-dimensional elasticity solution is very closely approximated. This holds for thin as well as rather thick plates with a slenderness ratio down to five. In contrast to many recently established methods, either higher order lamination theories or layerwise theories, the approach is easily applicable to finite elements, since only C0-continuity is necessary and the numerical effort is low.

KW - Fibre composite

KW - Interlaminar stresses

KW - Laminate

KW - Peeling stress

KW - Plate finite element

KW - Shear deformation theory

UR - http://www.scopus.com/inward/record.url?scp=0032166331&partnerID=8YFLogxK

U2 - 10.1016/S0045-7949(98)00097-2

DO - 10.1016/S0045-7949(98)00097-2

M3 - Article

AN - SCOPUS:0032166331

VL - 68

SP - 643

EP - 652

JO - Computers and Structures

JF - Computers and Structures

SN - 0045-7949

IS - 6

ER -