2D M ODELING OF THE D EFLECTION OF A S IMPLY S UPPORTED B EAM U NDER P OINT OR D ISTRIBUTED L OADS Y IN -Y U C HEN MANE4240 – I NTRODUCTION TO F INITE E LEMENT A NALYSIS A PRIL 28, 2014

Introduction/Background

Analytical Formulation/Solution

Modeling  COMSOL Multiphysics  2D Structural Mechanics, Solid Mechanics and Stationary presets  Rectangular geometry with prescribed displacements of 0m at bottom corners (x & y for one, y only for the other) to represent a simply supported beam  Point load case: N at center (x=4m)  Distributed load case: N/m  Mesh Extension Validation Extremely Fine Finer Normal Coarser Extremely Coarse

Results  Simply Supported Beam with Point Load at the Center  Simply Supported Beam with Uniformly Distributed Load

Results  Comparison of COMSOL Modeling/Numerical and Analytical Method Results  Comparison of ANSYS Modeling/Numerical and Analytical Method Results

Conclusions  Maximum deflection of a simply supported elastic beam subject to point or distributed loads may be achieved using either the modeling/numerical or analytical methods  Appears that the shape of the cells for the mesh is a major factor in the accuracy of the maximum beam deflection results Quadrilateral cell mesh may offer the most accurate solution  The steel beam requires a minimum height of 0.2m from the ground for the tank to avoid setting off the land mine  This study highlights necessity for verifying the reliability of the approximate solution by comparing the results to:  A theoretical/exact solution  A different modeling approach  A mesh extension validation If results from the COMSOL analysis of the uniformly distributed load across the beam were used without a factor of safety > 1.1 for the height of the beam from the ground, the maximum deflection due to the tank would set off the land mine