Loadvector

Loadvector is a term commonly used in finite element analysis and structural mechanics to denote the global vector of external nodal forces acting on a discretized domain. It aggregates contributions from body forces, surface tractions, and point loads, expressed in the global coordinate system and mapped to the system’s degrees of freedom.

In static problems, the finite element equations are written as KU = F, where K is the stiffness matrix, U is the vector of nodal displacements, and F is the load vector. In dynamic problems, the load vector may be time-dependent and appear on the right-hand side of equations such as MÜ + KU = F(t), with M the mass matrix and U the displacement vector.

Construction and assembly: For each element, a local nodal load vector is computed by integrating body forces over the element and applying surface tractions, then transforming these local loads to the global coordinate system using the element’s shape functions. The element contributions are then assembled into the global load vector F by adding them into the corresponding global degrees of freedom.

Boundary conditions and practical considerations: Essential (displacement) boundary conditions modify the global system and may require adjustments to both K and F to enforce prescribed values. For distributed loads, accurate evaluation of integrals over each element is important, especially for nonuniform load fields. Time-dependent loads are evaluated at each time step in dynamic analyses. The load vector is often referred to as the right-hand side or external force vector and is distinct from the internal response captured by the stiffness or mass matrices.