40207_32 - ANALYSIS METHODS V V Vasiliev 32 32.1...

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ANALYSIS METHODS ENUIRONMENTRL RNO CONDITIONS OPERRTI ONRL --+ 32 I + OUERRLL STRRINS RSSUMPTIONS GOUERNING RNO EQURTIONS OISPLRCEMENTS -b AN0 MOOELS * A I VV Vasiliev 32.1 INTRODUCTION A detailed analysis of composite structures can provide information about the stress-strain state, strength, stiffness, stability and vibra- tional behaviour of structural elements. The analytic methods are those used in solid mechanics; the equations are modified to reflect the structural behaviour of composite structures. These equations are based on a sys- tem of assumptions that take into account the key features of a structure and establish the appropriate model for the structural element under consideration. To start the analysis (Fig. 32.1), one must know the geometric configuration of the struc- ture, material properties, environmental and operational conditions along with the applied loads. It must be noted that the available data on material properties and loading conditions affect accuracy, duration and cost of the analy- sis. As an illustration, consider a cylindrical shell loaded with a concentrated radial force. The solution for this problem can be obtained EQUl LI BRI UM EQUATIONS LOROS I I STRAIN-DI SPLRCEMENT EOURTIONS r I I EXPERIMENTAL I- RNRLYSIS INLRMINRR CONSTlTUlTlUE STRENGTH - UERlFlCRTlON Handbook of Composites. Edited by S.T. Peters. Published in 1998 by Chapman & Hall, London. ISBN 0 412 54020 7 Fig. 32-1 Outline of analysis for composite StrUC- tures.
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in the form of a Fourier series that has a very poor convergence at the loaded point. However, a closer inspection of the loading conditions often shows that the concentrated force is the resultant of some distributed load over an infinitesimal area; this distributed load can then be expressed by the series with a finite number of terms to achieve convergence. Operational requirements for the composite structures are also of great importance. For example, a filament wound composite shell of revolution can be a model for either a gas pres- sure vessel or a solid propellant rocket motor case for which, in contrast to the pressure ves- sel, time dependent material properties need not be considered. On the basis of this knowl- edge, assumptions are formulated for the model of the structural component under study. This model should consider only the key factors affecting the capability of the struc- ture and ignore the secondary effects that complicate the analysis without significant improvement. The next step implies analytical formula- tion of the problem, i.e. development of a complete set of the governing equations with the pertinent boundary conditions. For struc- tural analysis, the governing set of equations consists of equilibrium equations (or equa- tions of motion), strain-displacement and the constitutive equations which are material dependent. The constitutive equations include stiffness coefficients which are determined by either of the following two methods: 0 The first method is associated with direct experimental analysis of test specimens cut out of the structure or its excess length. This
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40207_32 - ANALYSIS METHODS V V Vasiliev 32 32.1...

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