High-precision modelling of deformation of sandwich structures under bilateral symmetric and oblique-symmetric loading
DOI:
https://doi.org/10.32347/2410-2547.2024.112.258-267Keywords:
refined continual model, multilayered plate, transverse shear, transverse compressionAbstract
The analysis and assessment of the stress-strain state (STS) of multilayer plates with orthotropic layers under the action of stationary transverse and tangential loads is an urgent task. It includes calculations on the strength and deformability of various homogeneous and multi-layered plates with layers of constant thickness but arbitrary structure according to the thickness of the plate. Combining materials with isotropic and transversely isotropic physical characteristics into a multilayer package allows you to create multifunctional structures. The SSS of such structures, due to their structural heterogeneity and relatively low transverse stiffness of the individual layers, is significantly associated with the influence of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modeling of SSS plates, which would take into account these types of deformations, is urgent. Based on the decomposition of the SSS plate into flexural and unflexural components, it is proposed to optimize the design scheme of deformation of a rectangular multilayer plate. This significantly simplifies its modeling. For unflexural and exclusively flexural SSS, a two-dimensional, high-degree iterative approximation, but three-dimensional models of deformation of multilayer rectangular plate on a rigid foundation with isotropic, transverse-isotropic and orthotropic layers are constructed in an elastic formulation. That models takes full account deformation of transverse shear and transverse compression at transverse and the tangential loading of a plate. The model is continuous, that is, the number of equations and the order of differentiation of the calculation system of equations does not depend on the number of layers in the slab. This order of differentiation and the number of calculation equations can depend only on the order of iterative approximation of the model. A way of precise satisfaction of all defining correlations of the layers of material under keeping the conditions of their contact is found, while in the known continual models the dependence between the cross normal stress and cross deformation is only integral.The results of the analytical solution of the problem of deformation of a rectangular plate under boundary conditions of the Navier type under the action of transverse and tangential loads are given. By solving the test problems of the deformation of two-layer plates with transversally isotropic layers and three-layer plates with orthotropic layers and comparing the solutions with the exact three-dimensional solutions of these problems obtained by known methods, an assessment of the accuracy of the proposed refined models is given. The limits of admissible parameters of elastic characteristics of transversely isotropic and orthotropic plates for application of the offered models are established.
References
Piskunov V.G., Sipetov V.S., Tuymetov Sh.Sh. Resheniye zadach statiki dlya sloistykh ortotropnykh plit v prostranstvennoy postanovke [Solution of statics problems for layered orthotropic plates in a spatial setting (in Russian)] // Applied Mechanics. - 1990. - Vol. 26, N. 2. - P.41–49.
Prusakov A.P. K teorii izgiba sloistykh plastin [On the theory of bending of laminated plates (in Russian)]// Applied Mechanics. - 1997. - Vol.33, N. 3. – P. 64-70.
Rasskazov A.O., Burygina A.V. K utochneniiu teorii sdviga sloistykh pologikh obolochek [To the specification of shift theory of orthotropic hoping shells (in Russian)] // Applied Mechanics. – 1988. - Vol.24, N. 4. - P. 32-37.
Piskunov V.G. Rasskazov A.A. Teoriya sdviga vtorogo priblizheniya dlya mnogosloynykh pologikh obolochek i plastin [Shear theory of the second approximation for multilayer shallow shells and plates (in Russian)] // Mechanics of Composite Materials. – 1998. – Vol. 34, N.3. – P. 363–370.
Gurtovyi O.G., Piskunov V.G. Novyye raschetnyie modeli i sravneniye priblizhennykh utochnennykh s tochnymi trekhmernymi resheniyami zadach izgiba mnogosloynykh anizotropnykh plastin [New account patterns and comparison of approximate specified with exact three-dimensional solutions problems of the flexure laminated anisotropic plates (in Russian)] // Mechanics of Composite Materials. – 1988. – N. 1, P. 93-101.
Gurtovyi O.G. Vysokotochnoye modelirovaniye deformirovaniya sloistykh struktur [High-precision modeling of deformation of layered structures (in Russian)] // Mechanics of composite materials. – 1999. - V. 35, N. 1. - P. 13–28.
Gurtovyi O.G., Tynchuk S.O. Bezyzgibnaya utochnennaya model deformirovaniya mnogosloynykh plit na nedeformiruyemom osnovanii [An unflexural refined model of deformation of multilayer plates on an undeformable foundation (in Russian)] // Mechanics of composite materials. - 2006. - V. 42, № 5. - P. 643–654.
Piskunov V.G., Sipetov V.S. Raschet sloistykh pologikh obolochek iz anizotropnykh kompozitov na staticheskoye i temperaturnoye vozdeystviye [Calculation of laminated hoping shells of anisotropic composits for static and themperature action (in Russian)] // Problemy Prochnosti. – 1987. – N. 10, P. 79-82.
Piskunov V.G., Sipetov V.S. Utochnennaya model' raspredeleniya temperaturnogo rezhima dlya resheniya zadach termouprugosti mnogosloynykh sistem [A refined model of the temperature pattern distribution for solving the problems on thermoelasticity of the multilayer systems (in Russian) // Doklady Akademii Nauk Ukrainskoy SSR. – 1987. – N.5, P.49-52.
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