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In structural engineering, the direct stiffness method, also known as the matrix stiffness method, is a structural analysis technique particularly suited for computer-automated analysis of complex structures including the statically indeterminate type.
The full stiffness matrix A is the sum of the element stiffness matrices. In particular, for basis functions that are only supported locally, the stiffness matrix is sparse. For many standard choices of basis functions, i.e. piecewise linear basis functions on triangles, there are simple formulas for the element stiffness matrices.
The matrix method is a structural analysis method used as a fundamental principle in many applications in civil engineering. ... Direct stiffness method;
The matrix is usually referred to as the stiffness matrix, while the matrix is ... Direct stiffness method; Discontinuity layout optimization; Discrete element method;
When there are degrees of freedom a matrix must be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or ...
The origin of finite method can be traced to the matrix analysis of structures [1] [2] where the concept of a displacement or stiffness matrix approach was introduced. Finite element concepts were developed based on engineering methods in 1950s.
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Mathematically, this requires a stiffness matrix to have full rank. A statically indeterminate structure can only be analyzed by including further information like material properties and deflections. Numerically, this can be achieved by using matrix structural analyses, finite element method (FEM) or the moment distribution method (Hardy Cross) .