Tangent stiffness matrix
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In computational mechanics
Computational mechanics
Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science as a "third way" besides theoretical and experimental sciences, computational mechanics was widely...

, a tangent stiffness matrix is a matrix that describes the stiffness of a system in response to small changes in configuration. It represents tangent
Tangent
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

 in that the energy of the system can be thought of as a high-dimensional surface with the local slope of a plane tangent to it at the given point defined by the tangent stiffness matrix.

The tangent stiffness matrix appears when solving certain problems. For example, the tangent stiffness matrix is the generalization of slope that can be used with Newton's method
Newton's method
In numerical analysis, Newton's method , named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots of a real-valued function. The algorithm is first in the class of Householder's methods, succeeded by Halley's method...

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