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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 material stiffness properties of these elements are then, through linear algebra, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure’s unknown displacements and forces can then be determined by solving this equation.
For these reasons, the matrix stiffness method is the method of choice for use in general purpose structural analysis software packages. On the other hand, for linear systems with a low degree of statical indeterminacy, the flexibility method has the advantage of being computationally less intensive.
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.
Stiffness is the extent to which an object resists deformation in response to an applied force. [ 1 ] The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
Early applications of matrix methods were applied to articulated frameworks with truss, beam and column elements; later and more advanced matrix methods, referred to as "finite element analysis", model an entire structure with one-, two-, and three-dimensional elements and can be used for articulated systems together with continuous systems ...
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The stiffness of a structural element of a given material is the product of the material's Young's modulus and the element's second moment of area. Stiffness is measured in force per unit length (newtons per millimetre or N/mm), and is equivalent to the 'force constant' in Hooke's Law. The deflection of a structure under loading is dependent on ...