Finite Element Analysis

Use this for “A steel bar element 1,000 mm long has an area of 100 mm² and E = 200 GPa. Its nodes move 0.02 mm and 0.12 mm. Find k, the element force and the stress.”

Use this for “Springs of 1000 N/mm and 2000 N/mm hold node 2 between two walls, and 3000 N pushes it toward node 3. Find its displacement and both reactions.”

Use this for “A three-node element has nodal displacements 2, 30 and 50 μm at ξ = −1, 0 and 1. Find u at ξ = 0.5.”

Use this for “A bar element runs from x = 20 to 60 mm. Where is ξ = 0.5, and what is the Jacobian?”

Use this for “A truss element has AE ÷ L = 50,000 N/mm and lies at 30°. Find the terms of its 4 × 4 global stiffness matrix.”

Use this for “Model a 2 m cantilever, E = 200 GPa, I = 8 × 10⁶ mm⁴, as one beam element with 5 kN at its free end. Solve for v and θ.”

Use this for “A plate is meshed 10 × 5 with four-node quadrilaterals. How many nodes and degrees of freedom does the model have?”

Use this for “A mesh check flags an element with aspect ratio 15. Is it fine to use, or should the mesh be fixed?”

Use this for “The FEA peak sits at a sharp inside corner and grows each time the mesh is refined. Can I trust it?”

Use this for “A right-angled CST has node 1 at the origin pinned, node 2 at (40, 0) and node 3 at (0, 30) mm. Node 2 moves (12, 4) μm and node 3 (6, 9) μm. Find the strains.”

Use this for “A Q4 element is a parallelogram with a 60 mm base, 40 mm height and a 20 mm lean. Find J and det J, and check the area.”