The bar is a square bottom with a cross-section area of 0.01 \(m^2\) and the length of the bar is 1.0 \(m\). Point B is located at the middle of the edge AC and point E is at the middle of the edge DF.

The bar is released from a 45° angle (\(\theta_{start}\)) and the velocity at the free end of the bar at 180° (\(\theta_{end}\)) is compared with the analytical solution from the document above.

Analysis Type and Mesh

Tool Type: Code_Aster

Analysis Type: Dynamic

Mesh and Element Types:

The mesh for case A consists of 1\(^{st}\) order elements and it was created with the Standard meshing algorithm in SimScale with a region refinement applied.

The equations used to solve the problem are derived in [Schaum’s].

The constant of integration C is given by equation (1). It is then used to calculate the angular velocity at the free end of the bar in equation (2) with \(\theta_{start}\) = 45° and \(\theta_{end}\) = 180°. With the angular velocity, the magnitude of the velocity can be calculated with equation (3).

The magnitude of velocity (\(v\)) obtained then is 7.08803 \(m/s\).

Result Comparison

Comparison of the velocities obtained from SimScale against the reference results obtained from [Schaum’s]\(^1\) is given below:

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