jäykkyysmalli

Jäykkyysmalli, often translated as stiffness matrix or stiffness model, is a fundamental concept in structural mechanics and finite element analysis. It describes the relationship between the forces or moments applied to a structure and the resulting deformations or displacements. Essentially, it quantizes how resistant a structure is to being deformed.

The stiffness matrix is a mathematical representation, typically a square matrix, where each element quantifies the influence of a particular force or moment on a corresponding displacement or rotation at a different point in the structure. For a linear elastic material, this relationship is linear, meaning that doubling the applied force will double the resulting displacement. This linearity allows for the use of matrix algebra to solve complex structural problems.

In finite element analysis (FEA), a structure is discretized into smaller, simpler elements. Each element has its own stiffness matrix, which is then assembled into a global stiffness matrix representing the entire structure. By applying external loads and boundary conditions to this global stiffness matrix, engineers can solve for the displacements and stresses throughout the structure. Understanding and accurately defining the stiffness matrix is crucial for predicting the behavior of structures under various loading conditions, ensuring their safety and efficiency. It is a core component in the design and analysis of everything from bridges and buildings to aircraft and mechanical components.