FIRST COURSE FINITE ELEMENT METHOD COMPREHENSIVE PAPER 2026 BUNDLED EXPLANATIONS REVIEWED

FIRST COURSE FINITE ELEMENT METHOD
COMPREHENSIVE PAPER 2026 BUNDLED
EXPLANATIONS REVIEWED

⩥ Field Variable. Answer: The primary unknown that solves the problem
(e.g., displacement or temperature)


⩥ Degree of Freedom (DOF). Answer: The nodal value of the field
variable


⩥ Node. Answer: A location where the field variable is approximated


⩥ Element. Answer: A region formed by connecting nodes with an
interpolation function


⩥ Interpolation Equation. Answer: u~ = Nq


⩥ Shape Functions (N). Answer: Functions that define influence of each
node on the solution


⩥ Nodal Values (q). Answer: Vector of nodal degrees of freedom

, ⩥ Shape Function Requirement 1. Answer: Equals 1 at its own node


⩥ Shape Function Requirement 2. Answer: Equals 0 at all other nodes


⩥ Interpolation Meaning. Answer: Weighted sum of nodal values


⩥ Element Stiffness Equation. Answer: kq = f


⩥ Stiffness Matrix (k). Answer: Matrix relating nodal displacements to
forces


⩥ Force Vector (f). Answer: Vector of nodal forces


⩥ Potential Energy Principle. Answer: System is in equilibrium when
total potential energy is stationary


⩥ Equilibrium Condition. Answer: Derivatives of potential energy equal
zero


⩥ Result of PE Method. Answer: kq - f = 0


⩥ Residual (MWR). Answer: Error from approximate solution