Free and Forced Vibration Analyses by n-sided Polygonal Cell-based Strain-Smoothed Finite Element for Two-dimensional Problem
Keywords:
n-sided Polygonal element, Smoothed finite element, Cook’s beam, Free vibration, Periodic vibrationAbstract
Free and forced vibration analyses using n-sided polygonal element-based strain-smoothed finite element for two-dimensional problem is investigated for this research. Initialized with triangular elements discretization on problem domain like an old fashion finite element, an arbitrary n-sided polygon elements can be created by Delaunay triangulation algorithms for unstructured triangular mesh. Those polygonal elements will then be further partitioned into quadrilateral smoothing cells. A modified Cook beam with three holes which its left side is hinged while the opposite side is imposed to shear traction in vertical direction is an example for numerical simulation. Two types of analyses are performed namely free and transient vibration. Due to unavailable exact solutions, close-to-exact solutions obtained from very fine quadrilateral meshes finite element analysis are utilized instead. The former analysis investigates the first four natural frequencies and corresponding mode shapes of an example beam by soling an Eigenvalue problem. The results show in good agreement between polygonal smoothed finite element and reference solutions. The latter is forced periodic vibration analysis using implicit Newmark-Beta method comparing a vertical displacement at a particular point in specified duration of force dependent triangular time variation. The results are also in good shape with reference solutions at all periods of analysis time with few numbers of polygonal elements compared to a traditional one.
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