- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
The behavior and characteristics of classical membrane theory of isotropic materials are different from that of anisotropic materials, care must be taken to prevent secondary bending moments due to the unbalanced arrangement of laminates of anisotropic materials. At times, bending theory may have to be adopted and the current design codes, such as ASME, API and ACI must be reviewed for the case of anisotropic materials. The stresses and strains can be significantly different between the pure membrane and bending theories. This paper derives a membrane type shell theory of hybrid anisotropic materials, governing differential equations together with the procedures to locate the mechanical neutral axis. The theory is derived by first considering generalized stress strain relationship of a three dimensional anisotropic body which is subjected to 21 compliance matrix and then non-dimensionalizing each variable with asymptotic expansion. After applying to the equilibrium and stress-displacement equations, we are allowed to proceed asymptotic integration to reach the first approximation theory. Also possible secondary moments due to the unbalanced built up of lamination are quantifiably expressed. The theory is different from the so called pure membrane or the semi-membrane analysis.
In the present analysis, first approximation shell theories are derived by use of the method of asymptotic integration of the exact three-dimensional elasticity equations for a non-homogeneous anisotropic circular cylindrical shell. The analysis is valid for materials which are non-homogeneous to the extent that their properties are allowed to vary with the thickness coordinate (r). The first approximation theory derived in this analysis represent the simplest possible shell theories for the corresponding length scales considered. Although twenty-one elastic coefficients are present in the original formulation of the problem, only six are appear in the first approximation theories. It was seen that use of the asymptotic method employed in the research also yields expressions for all stress components, including the transverse ones. Unlike the pure membrane theory of isotropic materials, secondary bending moments can be computed in association of material characteristics of lamination. The fact that these expressions can be determined is very useful when discussing the possible failure of composite shells and also for the discrepancy between theoretical membrane theory and experimental results. For design of space shuttles and other vehicles, a shell structure must be carefully designed for all possible loading conditions, extremely high negative and positive pressure and temperature, which demands further accurate shell theories. In case the membrane theory seems to be justified, the effect of all possible secondary bending moments must carefully be examined as shown in the Eq. (37) through (41) of this analysis. It is more realistic for shells of hybrid anisotropic materials of high strength.