验证例题35.pdf

1Example 35 Title Behaviors of a cantilever beam under concentrated loads at the free end Description Examine the static&dynamic behaviors of a cantilever beam.Compare the results based on the models composed of solid elements and beam elements.Structural analysis model and load cases Verification Example 2Model Analysis Type 3-D eigenvalue analysis Unit System m,tonf Dimension Length 5 m Element Solid element Material Concrete Modulus of elasticity E=2.1 106 tonf/m2 Poissons ratio =0.167 Weight density =2.4 tonf/m3 Boundary Condition Nodes 1,2,3 and 4;Constrain all DOFs.Load Case A concentrated load,1 tonf is applied to each of the nodes 41,42,43 and 44 at the free end.The load cases 1,2 and 3 represent the loads acting in the directions of X,Y and Z respectively.Analysis Case Self weight is converted to nodal masses automatically.Number of natural frequencies to be computed=10 Example 35 3Results Displacements (Solid element)Eigenvalue Analysis Results(Solid element)Verification Example 4Comparison of Results Displacements Unit:m Load Case NISA II(Solid elements)MIDAS/Gen(Beam elements)MIDAS/Gen(Solid elements)LDC 1(X direction)9.505E-06 9.524E-06 9.505E-06 LDC 2(Y direction)0.003810 0.003836 0.003810 LDC 3(Z direction)0.003810 0.003836 0.003810 Natural Periods Unit:sec Natural Period NISA II(Solid elements)MIDAS/Gen(Beam elements)MIDAS/Gen(Solid elements)1st mode 0.1068087 0.1067212 0.1068097 4thmode 0.0180404 0.0177576 0.0180404 6thmode 0.0069252 0.0067133 0.0069252 8thmode 0.0068223 0.0068348 0.0068223 Reference Tomas J.R.Hughes,“The Finite Element Method”,Chapter 3