A Comparative Study Between Finite Element and Polygonal Finite Element Approaches for Electromechanical Coupled Linear Problems

Convergence and accuracy of displacement based finite element formulations over arbitrary polygons: Laplace interpolants, strain smoothing and scaled boundary polygon formulation

“…Owing to symmetry, only one quarter of the plate is modeled. Figure (12) shows a typical polygonal mesh used for the study. The material properties are: Young's modulus E = 10 5 and Poisson's ratio ν = 0.3.…”

“…On another, related front, generalizations of FEM on arbitrary polygonal and polyhedral meshes have been the subject of increasing attention in the research community, both in computational physics [9,10,11,12,13,14] and in computer graphics [15,16].…”

“…Kraus et al, [14] presented a polygonal FEM based on the constrained adaptive Delaunay tessellation. The polygonal elements can also be used as transition elements to simplify meshing or to describe the microstructure of polycrystalline alloys [11,12,13] in a rather straightforward manner. However, approximation functions on polygonal elements are usually nonpolynomial, which introduces difficulties in numerical integration.…”

Error estimation for the polygonal finite element method for smooth and singular linear elasticity

“…The earlier studies were restricted to quadrilateral and triangular elements in two dimensions and, tetrahedral and hexahedral elements in three dimensions. Recently, finite elements in the shape of pentagons, hexagons and in general n−sided polygons (and polyhedral elements in three dimensions) have attracted attention in the research community, both in computational physics [11][12][13][14][15][16] and in computer graphics [17,18]. In the early 1970s, Wachspress derived a systematic approach to construct basis functions over arbitrary polygonal domains in his famous book on the rational finite element method [19].…”

Properties of Three Phase Magneto-Electro-Thermo-Elastic Composites

“…The use of smart materials, which exhibits electric-mechanical coupling (piezoelectric) and magneticmechanical coupling (piezomagnetic) is rapidly increasing in engineering applications [1,2]. Magnetoelectro-thermo-elastic (METE) composites, that consists of piezoelectric and piezomagnetic phases exhibits a new coupling phenomena called as magnetoelectric (ME) effect, which cannot be found in either of the individual phase [3].…”