Checking elements 13 and 2 by FEA (ANSYS) — example

1. Analysis model and input data

Analysis model

Analysis model in the XYZ coordinate system of the ATD

Analysis model in the ANSYS coordinate system

Input data

Forces: F_X = 1500 N, F_Y = 300 N, F_Z = 700 N.

Geometric parameters: X₁ = 80 mm, X₂ = 220 mm, X₃ = 150 mm, Y₁ = 550 mm, Z₁ = 180 mm, Z₂ = 250 mm; L_Y = 120 mm; L_c = 70 mm; b₂ = 120 mm; b₁₃ = 120 mm; g₂ = 10 mm; g₁₃ = 15 mm; h₁₂ = 50 mm; R = 20 mm.

Material: S235, weldable general-purpose steel, for element 13; E335, steel for mechanical construction, for element 2.

Operating constraints: temperature T = (−30…40) °C.

Parameters of the ANSYS model

Forces: F_x = F_Y/2 = 150 N, F_y = −F_Z/2 = −350 N, F_z = F_X/2 = 750 N.

Geometric parameters: h13 = g₁₃ = 15 mm, h3 = g₂ = 10 mm, b13 = b₁₃ = 120 mm, L7 = 190 mm, L_Y = 120 mm, Ri = R = 20 mm, Re = R + g₂ = 30 mm, h12 = h₁₂ = 50 mm; L1 = 35 mm, L2 = 35 mm; FD1 = 120 mm for Element 2 and FD1 = 270 mm for Element 13; coordinates of the force application point: XCoordinate = Y₁ + g13 = 565 mm; YCoordinate = Z₁ + L_c = 250 mm; ZCoordinate = X₁ + X₂ + X₃ + b₂/2 = 510 mm.

Material: for S235 steel, σ_at = σ₀₂/c = 235/1.3 = 180 MPa (since the FEA model is more accurate, a lower safety factor c = 1.3 was adopted than for the classical, less accurate design models, where usually c > 2); for E335 steel, σ_at = σ₀₂/c = 335/1.3 ≈ 250 MPa; allowable contact stresses: σ_as = 90 MPa, the allowable steel-on-steel normal crushing stress, and τ_as = 45 MPa, the allowable steel-on-steel tangential contact stress.

Viewing the support (fixed) zone and the applied forces and moments

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2. Results

Viewing the forces in the reaction zone

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Viewing the displacements

🖱 → the model appears

Viewing the stresses

Equivalent stresses on the global model

🖱 → the model appears

Equivalent stresses on the model of Element 13

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Equivalent stresses on the model of Element 2

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Viewing the pressures and stresses in the contact zones

Pressures on the contact surfaces

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Friction stresses on the contact surfaces

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3. Checks

Stiffness (deflection) check

δ ≤ δ_a; 6.19 ≤ 10 mm (satisfied).

Note. The allowable deflection is set by the operating conditions.

Check under combined loading

σ_{ech_max} ≤ σ_at; 302.65 ≤ 196 MPa (NOT satisfied),

where σ_{ech_max} is the maximum equivalent stress in the figure above.

If the inequality above is NOT satisfied, one of the following options can be chosen:

a. choose a better material;

b. change the geometry by increasing one or more dimensions;

c. choose another material and change the geometry.

In this application, option b is adopted and the analysis steps are repeated, as detailed below.

Changing the geometric parameters

Activating the DesignModeler module

🖱🖱 → the window opens with the geometric model.

Changing the section dimensions

🖱 → 🖱 → : [change the dimension h3].

Saving the model

🖱 → 🖱.

Updating the geometric model in the FEA model

🖱 → → 🖱

Solving the modified model

→ 🖱.

Post-processing the modified model

Equivalent stresses on the global model

🖱 → the model appears.

Re-check under combined loading

σ_{ech_max} ≤ σ_at; 121.73 ≤ 180 MPa (satisfied), where σ_{ech_max} is the maximum equivalent stress in the figure above.

Check of the normal contact pressure

p_max ≤ σ_as; 30.131 ≤ 90 MPa (satisfied),

where p_max is the maximum pressure in the figure above.

Check of the tangential (friction) contact stress

τ_max ≤ τ_as; 40.909 ≤ 45 MPa (satisfied),

where τ_max is the maximum tangential contact stress (frictional stress) in the figure above and τ_as the allowable tangential contact stress.