Numerical-analytical method of analysis of metal-composite pressure cylinder
Mathematics. Physics. Mechanics
Bauman Moscow State Technical University, MSTU, 5, 2-nd Baumanskaya, Moscow, 105005, Russia
High-pressure cylinders consisting of an inner hermetic metallic enclosure (liner) and an outer force composite shell from carbon-filled plastic are widely used in space engineering. We suggest a numerical-analytical method of calculating the cylindrical part of a metal-composite pressure cylinder. The method takes into consideration non-linear deformation curve of the liner and structure in homogeneity of the linearly elastic composite shell. Solution of the problem in this formulation is based on the method of successive loading and on the model of an ideal elastoplastic liner at each loading step. Multilayer composite shell is considered to be orthotropic with longitudinal, circumferential and shear-generalized rigidity. Experimental deformation curve of the liner is replaced by specially built analytic approximating polynomial function; this makes it possible to automate calculations.
Algorithm of the metal-composite cylinder calculation in cludes two schemes. According to the first scheme, the composite shell and the liner are madelinearly elastic, and from it we search out the pressure which value corresponds to the limit of proportionality of the liner material. In the second scheme, the composite shell is linearly elastic, and plastic deformations occur in the liner. The second scheme is applied at each loading step of the cylinder; thereto the liner deformation diagram is represented in a step function, ordinates of which are taken from the analytically derived deformation curve, and the length of «the stepping yield plateau» (by strains) is determined by the increment of pressure.
This internal pressure calculation algorithm for a metal-composite cylinder is implemented as a program in MatLAB. The numerical investigations have shown that the accuracy of the results increases with then umber of loading steps. In the article we gave a computation example of the metal-composite pressure cylinder consisting of the liner from the alloy AMg-6 and the carbon fiber shell with spiral and annular layers. We established that 15 steps of loading were enough to achieve sufficient accuracy for practical problems. The longitudinal and circumferential stress and strain in the liner reduced, and had horizontal asymptotes. The program developed for determining the stress-strain state of metal-composite pressure cylinders can be effectively used for designing calculations.
Keywords:metal-composite pressure cylinder, analysis, calculation, mode of deformation, liner, non-linear deformation curve
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