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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
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.
A linear constant coefficient system is stiff if all of its eigenvalues have negative real part and the stiffness ratio is large. Stiffness occurs when stability requirements, rather than those of accuracy, constrain the step length. Stiffness occurs when some components of the solution decay much more rapidly than others. [3]
The first step when using the direct stiffness method is to identify the individual elements which make up the structure. Once the elements are identified, the structure is disconnected at the nodes, the points which connect the different elements together. Each element is then analyzed individually to develop member stiffness equations.
A spring system can be thought of as the simplest case of the finite element method for solving problems in statics. Assuming linear springs and small deformation (or restricting to one-dimensional motion) a spring system can be cast as a (possibly overdetermined) system of linear equations or equivalently as an energy minimization problem.
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 Newmark-beta method is a method of numerical integration used to solve certain differential equations.It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems.
Stiffness depends upon material properties and geometry. 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.
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