验证例题04.pdf

1Example 4 Title Circular ring structure Description A circular ring is subjected to a pair of equal and opposite concentrated loads in the radial direction of the ring.Determine the displacements and bending moments.Only a quarter of the model may be analyzed due to symmetry.2 Structural geometry and analysis model Example 60 3Model Analysis Type 2-D static analysis(X-Z plane)Unit System m,N Dimension Radius 2.0 m Thickness 0.0004 m Width 1.0 m Element Beam element Material Modulus of elasticity E =2.0 1011 Pa Section Property Area A =4.0 10-4 m2 Effective shear area Asz=2.66667 10-4 m2 Moment of inertia Iyy =1.33333 10-8 m4 Boundary Condition Node 1 ;Constrain Dz and Ry.(Symmetric about X-axis)Node 13 ;Constrain Dx and Ry.(Symmetric about Z-axis)Load Case With a quarter model a load,8.0/2 N,is applied to the node 13 in the-Z direction.4Results Deformed shape of the structure Bending moment diagram of the structure Example 60 5Comparison of Results Unit:m,Nm Results Theoretical ADINA MIDAS/Gen x(Node 13)1.6410-3 1.6310-3 1.6310-3 Displacement z(Node 13)-1.7910-3-1.7810-3-1.7810-3 Bending moment My(Node 13)5.09 5.09 5.09 References Timoshenko,S.,“Strength of Materials,Part I,Elementary Theory and Problems”,3rd Edition,D.Van Nostrand,1955.“ADINA,Verification Manual-Linear Problems”,Version 6.1,ADINA R&D,Inc.,1992,Example A.10.