Smoothed Finite Element using three smoothing domains created by arbitrary quadrilateral elements for Two-Dimensional Plane Stress Problem
Keywords:
Smoothed finite element, Sub-cell smoothing domains, Strain gradient, Two-dimensional plane stress, Cantilever beamAbstract
The alternative way to create sub-smoothing domains within an element for smoothed finite element analysis was proposed in this research. Three sub-cell smoothing domains were established continuously with the utilization of symmetrical pattern over the entire problem domain. Strain gradient technique is the most important key to distribute strain field smoothly within smoothing domain. Two-dimensional plane stress problem employed for this research was a cantilever beam subjected to parabola shear force with a maximum magnitude of 1000 unit at free end. Two control parameters were used. The first one is meshing ranging from coarse mesh 16x4 to finer mesh 48x12 as the same 4:1 ratio of horizontal to vertical dimension of beam. The latter is measured as fracture of an element side. The values of were 0.2-0.3, 0.3-0.4 and 0.4-0.5 respectively. Numerically evaluated normal and shear stresses over the cross-section area at the middle span and displacement at free end were compared to the exact solutions accordingly. Obviously, the free end displacement accuracy strongly influenced by the second control parameter. The normal stresses at equal to 0.3-0.4 and 0.4-0.5 compared to the exact solutions were found to be at the same accuracy while shear stresses were found to be dependent on mesh size than the value of .
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