1. Introduction#
The modeling of the thermo-mechanical behavior by a shell theory of structures made of laminated composite materials presents a certain number of particularities compared to the isotropic homogeneous case:
the coefficients involved in the linear behavioral relationships linking the mechanical and thermal quantities defined on the mean surface of the shell must be calculated from the spatial distribution in the thickness of the various materials,
the materials constituting the shell are generally orthotropic:
it is necessary to define, at each point on the mean surface of the shell, a material direction fixing the frame of reference in which the behavioral relationships are described,
the shape of the anisotropy produced on the overall behavior of the shell may be any,
finally, couplings between quantities characterizing symmetric and antisymmetric phenomena with respect to the mean surface may appear (flexion-membrane coupling, mean temperature-mean gradient coupling in the thickness). In thermo-mechanics, however, the results presented are theoretically valid only when the membrane-flexure coupling is zero,
the analysis of the breakage or damage of these structures requires a return to a level of description that is finer than that provided by shell models: the criteria are formulated, layer by layer in thickness, according to « three-dimensional » constraints.
Pre-processing allows the user to « build » the quantities involved in shell theories from a simple spatial description of the distribution of the various materials (position, thickness, orientation).
Post-treatment takes place once the structural calculation is complete to provide, layer by layer, an evaluation of some failure or damage criteria.
The bias here is to specify pre and post-treatments so that they are independent, within the framework of the shell models selected, from the type of element chosen by the user to perform the structure calculation. In fact, the numerical difficulties in calculating shells and representing their geometry lead to the proposal of several types of finite shell or plate elements, depending on the situation.
The note is divided into three parts. The first briefly recalls the hypotheses of shell theory used for thermo-mechanical calculations and the expressions of homogenized coefficients to be introduced. The second specifies the choices used for the description of the orientation of the materials in relation to the elements as well as some notations. The last part details the application of these choices in the case of shells made up of homogeneous strata.
To allow the use of the calculation options available in Code_Aster, it is therefore necessary to define pre and post-processing commands for laminated composite materials compatible with existing orders.