jäykkyysmatriisi

jäykkyysmatriisi is a concept in structural engineering and finite element analysis. It is a fundamental matrix that describes the relationship between the forces applied to a structure and the resulting displacements or deformations. Essentially, it quantizes how "stiff" a structure is.

The stiffness matrix, often denoted by K, is a square matrix where the number of rows and columns equals the number of degrees of freedom of the system being analyzed. Each element Kij represents the force that develops in degree of freedom i when a unit displacement is applied to degree of freedom j, while all other degrees of freedom are held fixed. A larger value in the stiffness matrix indicates a stronger resistance to deformation in that particular direction.

In finite element analysis, a structure is discretized into smaller elements. The stiffness matrix for the entire structure is assembled by combining the stiffness matrices of these individual elements. This global stiffness matrix is then used in the equation Ku = F, where K is the stiffness matrix, u is the vector of unknown nodal displacements, and F is the vector of applied nodal forces. Solving this equation allows engineers to determine how a structure will deform under various loading conditions, which is crucial for ensuring its safety and stability.