Incompatible Graded Finite Elements for Orthotropic Nonhomogeneous Media
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pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205
DOI 10.1007/s12205-020-0444-0
Structural Engineering
Incompatible Graded Finite Elements for Orthotropic Nonhomogeneous Media Asmita Rokayaa, Gokhan Egilmezb, and Jeongho Kima Dept. of Civil and Environmental Engineering, University of Connecticut, Storrs, CT 06269, USA Dept. of Mechanical and Industrial Engineering, University of New Haven, West Haven, CT 06516, USA
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ARTICLE HISTORY
ABSTRACT
Received 11 March 2020 Accepted 21 July 2020 Published Online 25 September 2020
Orthotropic materials or composites are challenging to model due to different elastic properties in two in-plane directions, which requires sufficient mesh refinement to attain desired accuracy. In this regard, an accurate and efficient incompatible graded element is developed for modeling orthotropic functionally graded materials. Properties of Graded finite elements such as Young’s moduli (E11, E22), shear modulus (G12) and Poisson’s ratio (v12) vary. A new incompatible graded element is developed using user subroutines in Abaqus and are compared to available exact solutions. In this study, performance (QM6) graded element is compared with lower-order and higher-order compatible elements (Q4 and Q8) as well as linear triangular (T3) and quadratic triangular (T6) elements with aid of several numerical examples. Additionally, orthotropic graded plate with carbon fibers properties as well as a circular disc with orthotropic properties under internal pressure is included. Furthermore, a curved beam with radially graded properties under the bending moment is studied. Additionally, the performance of various graded elements is compared with analytical solutions using Russell error.
KEYWORDS Graded elements QM6 incompatible element Functionally graded materials Error estimation Orthotropic materials
1. Introduction Functionally graded elements are non-homogenous and are designed to have variation of properties in space. The progressive variation of properties, aids in reducing thermal and residual stresses. Due to their advantages, extensive research has been done to explore thermal and mechanical properties of functionally graded materials (FGMs). Owing to the processing techniques such as plasma spray (Sampath et al., 1995), electron beam vapor deposition (Kaysser and Ilschner, 1995), functionally graded materials tend to orthotropic (Rao and Rahman, 2003). So far, considerable studies related to orthotropic functionally graded materials have been done (Shimpi and Patel, 2006). Investigation of fracture mechanics of orthotropic graded elements is done in (Kim and Paulino, 2002a). In these studies, several formulations for the evaluation of fracture parameters of orthotropic plates are developed. Additive manufacturing is one of the areas of an application of orthotropic FGMs. Functionally graded additive manufacturing allows changes in material properties with the position which CORRESPONDENCE Jeongho Kim
[email protected]
ⓒ 2020 Korean Society of Civil Engineers
can produce
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