The direct stiffness method is the displacement-based finite element assembly procedure that forms a global stiffness system from element stiffness matrices, applies boundary conditions, solves for nodal displacements, and recovers element forces, strains, or stresses.
How It Works
The method begins with an element relation between nodal force and nodal displacement. For a structure, element matrices are transformed to the global coordinate system when needed, mapped into global degrees of freedom, and superposed into the global system.
The introductory spring element is used to show the core logic: define element degrees of freedom, choose a displacement function, derive the element stiffness matrix, assemble the total stiffness matrix, impose homogeneous or nonhomogeneous boundary conditions, solve the reduced equations, and compute reactions or internal forces.
Why It Matters
The direct stiffness method is the practical bridge from element derivation to finite element software. It is simple enough to demonstrate by hand for spring, bar, truss, beam, and frame assemblages, yet it is also the same structural pattern used inside larger finite element programs.
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