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# FEA (Finite Element Analysis)

The objective of finite element analysis is to accurately determine the response of a system modeled with finite elements and subjected to given loads. 3D models are meshed into a system of 3D tetrahedral elements, the corners of which are called nodes. Nodal forces and stiffnesses are known quantities, and are grouped into a force matrix {F} and stiffness matrix [K]. The force matrix {F} is equal to the displacement matrix {U} times the stiffness matrix [K], or {F} = [K]{U}. Since the displacement matrix {U} is unknown, it is determined by solding the equation {U} = {F}[K]^-1 ([K]^-1 = inverse of the stiffness matrix). Displacemant is related to material strain (ε) which is used with the modulus of elasticity (E) to determine stress in the part σ with the equation σ= (ε)(E). This forms the basis of finite element analysis.

SOLIDWORKS Simulation uses the displacement formulation of the finite element method to calculate component displacements, strains, and stresses under internal and external loads.

#### Slideshow Explanation

Slide 1. The 'Tent Structure FEA' is a stress analysis of a commercial tent frame which is subjected to a wind                   load of 120 mph.
Slide 2.The 'Lifting Hook FEA' is a standard lifting hook stress analyzed while subjected to a load of 5 kips.
Slide 3.The 'Instrumented Pressure Vessel FEA' is a stress analysis of a IPV subjected to an external pressure of                 2234 psi, corresponding to a water depth of 5000 ft.
Slide 4.The 'Armored Cable Termination FEA' is a stress analysis of the ACT while it is subjected to a load of 10 kips                  (44.5 kn).

#### What FEA Can Do For You

FEA can be used to calculate stress and deflection in machine parts, assemblies, weldments, and sheet metal parts.

Stress values are compared to material ultimate or yield strength values to determine whether or not the part will be able to function as required.