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
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
