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TEST CASE 4.5 CONSOLE BENDING TO CYLINDER SURFACE FORMING

Reference:

L.D. Landau, E.M. Lifshitz. Course of Theoretical Physics. In 10 Volumes. Vol. VII. Theory of Elasticity – 4th edition. – М.: Nauka, 1987, p. 106

 

Problem description:

Console bar is loaded by bending moment Му at point B. Determine vertical displacement value w and horizontal displacement value u at point B. Find also horizontal displacement value u at the centre of bar span.

 

Problem sketch:

Type of created problem:

Spatial structure (X, Y, Z, UX, UY, UZ).

 

Geometric characteristics:

L = 10 m; b = 1 m; h = 0.01 mm.

 

Material properties:

Elastic modulus: E = 1.2·108 tf/m2.

 

Boundary conditions:

Point А: X = Y = Z = UX = UY = UZ = 0.

 

Loads:

My = 2π tf·m.

 

Model description:

The system is modeled via 100 geometrically nonlinear elements of tight bend bar (FE type is 309). Automatic selection of step of loading applying for nonlinear problem solution is used.

 

Calculation results:

Target value

Analytical solution

LIRA 10

Deviation, %

wВ, m

0.00

-0.0433

uВ, m

-10.00

-10.042

0.42

uL/2, m

-5.00

-5.0001

0.002

 

Vertical displacements distribution w, m

 

Horizontal displacements distribution u, m