Material orientation design of planar structures with prescribed anisotropy classes. Study of rhombic systems | Zendy

Radosław Czubacki | Zendy

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Material orientation design of planar structures with prescribed anisotropy classes. Study of rhombic systems

Author(s) -

Radosław Czubacki

Publication year - 2018

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.5019032

Subject(s) - orthotropic material , isoperimetric inequality , isotropy , anisotropy , planar , orientation (vector space) , material design , material properties , geometry , tensor (intrinsic definition) , materials science , mathematical analysis , structural engineering , mathematics , computer science , optics , physics , composite material , engineering , finite element method , computer graphics (images)

The paper deals with the minimum compliance problem of 2D structures made of a non-homogeneous elastic material. In the first part of the paper a comparison between solutions of Free Material Design (FMD), Cubic Material Design (CMD) and Isotropic Material Design (IMD) is shown for a simply supported plate in a shape of a deep beam, subjected to a concentrated in-plane force at its upper face. The isoperimetric condition fixes the value of the cost of the design expressed as the integral of the trace of the Hooke tensor. In the second part of the paper the material design approaches are extended to rhombic system in 2D. For the rhombic system the material properties of the structures are set, the design variables being the trajectories of anisotropy directions which in 2D are described by one parameter. In the Orthotropic Orientation Design (OOD) no isoperimetric condition is used.

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