Search results
Results from the WOW.Com Content Network
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.
After developing the element stiffness matrix in the global coordinate system, they must be merged into a single “master” or “global” stiffness matrix. When merging these matrices together there are two rules that must be followed: compatibility of displacements and force equilibrium at each node.
Physically, taking into account the added mechanisms of deformation effectively lowers the stiffness of the beam, while the result is a larger deflection under a static load and lower predicted eigenfrequencies for a given set of boundary conditions. The latter effect is more noticeable for higher frequencies as the wavelength becomes shorter ...
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
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.
The stiffness matrix components corresponding to each degree of freedom are determined by assuming a unit displacement in the studied direction and by determining forces at the centroid of each element. The 2D element stiffness matrix size is 6 × 6; the components of the upper left quarter of the stiffness matrix are shown below:
Flexibility is the inverse of stiffness. For example, consider a spring that has Q and q as, respectively, its force and deformation: The spring stiffness relation is Q = k q where k is the spring stiffness. Its flexibility relation is q = f Q, where f is the spring flexibility. Hence, f = 1/k.