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ISSN (print) 2542-2324 /(online) 2618-8244

Articles of The Transactions of KSRC

Bending model for a layered composite round plate.

Full text article ( in russian)










Bending model for a layered composite round plate.


D.A. Bartadim, V.S. Yakovlev


multilayer orthotropic plate, load-carrying stiff layers, interlayers, local effects, quasi-monolith plate, mathematic model, interlayer shift, deflection, stresses, ultimate load


Classical theories of multilayer plates are based on either kinematic (or static) hypotheses for a lay-up of the whole plate or hypotheses formulated for each layer separately. Within the first approach models do not permit to consider all specific features of multilayer plate deformation. Within the second approach the solving process is complicated by a great number of resolving equations.
A model having advantages of the both approaches is proposed.
The concept of the model generation is as follows. A plate with regularly alternating stiff layers and soft interlayers is considered. The stiff layer kinematics is described by Kirchhoff hypotheses; the soft interlayer kinematics is described by Bolotin hypotheses. The package is considered as absolutely stiff in the transverse direction. It follows from the comparison of the displacements w in the transverse direction obtained by the first approach and displacements w1 found by the second approach that they differ by magnitude wс caused by presence of interlayers compliant to inter-layer shear, as well as the position of the unified normal θ = w' differs from the layer normal θ1 = w1' by magnitude φ0= wс'. Therefore, points of k-th layers lying on broken normal θ1 could be superposed with the unified normal for the package as a whole through normal rotation by angle φ0 and normal shifting as a whole by a value proportional to the distance from the neutral bending plane. In the result the model is reduced to solving a problem of the refined theory of a quasi-monolithic plate with further definition of points’ positions on the broken normal with account of local effects due to deformation of discretely disposed layers. It should be noted that such an approach is possible only for layered plated of regular structure in the absence of layers’ and interlayers’ compression.
A mathematic model for a multilayer orthotropic round plate was generated in compliance with the stated concept. The results of the numerical experiment with test problems demonstrated good coincidence with the results obtained with the use of the second approach theories. Analysis of strained state evolution for a multilayer plate loaded by distributed transverse and radial forces was performed based on the developed model.


Naval architecture

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ISSN (print) 2542-2324 / ISSN (online) 2618-8244

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