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Bending of Orthotropic Plate Containing a Crack Parallel to the Median Plane

Shvabyuk V., Pasternak I., Sulym H.

Acta Mechanica et Automatica

2011

Vol. 5, no. 4

94-102

This paper considers cylindrical bending of the plate containing a crack parallel to plate's faces. The analytical model of the problem is obtained using the improved theory of plates bending, which considers transverse deformation of the plate. Received analytical results are compared with the numerical data of the boundary element approach, which is modified to suit the considered contact problem. The results of analytical and numerical techniques are in a good agreement both for the isotropic and anisotropic plates.

Shaping the stiffest three-dimensional structures from two given isotropic materials.

Czarnecki S., Lewiński T.

Computer Assisted Mechanics and Engineering Sciences

2006

Vol. 13, No. 1

53-83

The paper concerns layout optimization of elastic three dimensional bodies composed of two isotropic materials of given amount. Optimal distribution of the materials corresponds to minimization of the total compliance or the work of the given design-independent loading. The problem is discussed in its relaxed form admitting composite domains, according to the known theoretical results on making the minimum compliance problems well posed. The approach is based upon explicit formulae for the components of Hooke's tensor of the third rank stiff two material composites. An appropriate derivation of these formulae is provided. The numerical algorithm is based on COC concept, the equilibrium problems being solved by the ABAQUS system. Some of the optimal layouts presented compare favourably with the known benchmark solutions. The paper shows how to use commercial FEM codes to find optimal composite designs within linear elasticity theory.

The numerical verification of the bending composite model

Kobza W.

Zeszyty Naukowe. Włókiennictwo / Politechnika Łódzka

2000

z. 58

79-87

The classical theory of bending neglects the interaction between longitudinal layers and assumes their constant thickness independently of the magnitude of load. The theory is successfully applied for isotropic materials. In this work the model of bending multilayers composites materials filled with soft materiais such as for example honeycomb, porous materials or distance textile is described. The bending layers are compressed in transverse direction and theirs thickness and stiffness of bending decrease. The model of bending is numerically verified using an energetic finite element method.