Finite element analysis in ABAQUS, convergence and element formulation

Context

Individual first-year Master's lab in MESI (Finite Elements module), supervised by Dr Salah Elbarnaty and Prof. J.P.M. Correia. A 2 m cantilevered steel beam takes 250 N at its tip. The task was to compare ABAQUS with the analytical solution and understand the role of the mesh and the element type.

What I did

• Analytical reference (Euler-Bernoulli), maximum stress of ±75 MPa and deflection of 4.762 mm.
• ABAQUS model in plane stress, duplicated over eight configurations.
• Four meshes (1×6 to 8×24) crossed with two elements (linear CPS4, quadratic CPS8).
• For each case, stress, deformed shape, reactions and error on the deflection.

What I noticed and learned

• Choosing the right formulation matters more than refining the mesh blindly.
• Shear locking makes coarse CPS4 meshes too stiff, and the deflection is underestimated by 40%.

My mistakes

• I only handled a linear case, with no plasticity or contact. Yet that is where ABAQUS becomes essential.

Results

• 0.33% error with 6 CPS8 elements, against 0.94% with 192 CPS4 elements.
• With CPS4, convergence is slow, from 40.7% error at 1×6 to 0.94% at 8×24.
• Support reaction always equal to 250 N, checked in every case.

Tech stack