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Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges; Rigidity (electromagnetism), the resistance of a charged particle to deflection by a magnetic field; Rigidity (mathematics), a property of a collection of mathematical objects (for instance sets or functions)
Rigidity is an ancient part of our human cognition. [4] Systematic research on rigidity can be found tracing back to Gestalt psychologists, going as far back as the late 19th to early 20th century with Max Wertheimer, Wolfgang Köhler, and Kurt Koffka in Germany.
Mostow's rigidity theorem, which states that the geometric structure of negatively curved manifolds is determined by their topological structure. A well-ordered set is rigid in the sense that the only ( order-preserving ) automorphism on it is the identity function.
Rigidity is the property of a structure that it does not bend or flex under an applied force. The opposite of rigidity is flexibility.In structural rigidity theory, structures are formed by collections of objects that are themselves rigid bodies, often assumed to take simple geometric forms such as straight rods (line segments), with pairs of objects connected by flexible hinges.
Flexural rigidity is defined as the force couple required to bend a fixed non-rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending. Flexural rigidity of a beam
is the rigidity modulus of the material, J {\displaystyle J} is the torsion constant for the section. Note that the torsional stiffness has dimensions [force] * [length] / [angle], so that its SI units are N*m/rad.
In physics, a rigid body, also known as a rigid object, [2] is a solid body in which deformation is zero or negligible. The distance between any two given points on a rigid body remains constant in time regardless of external forces or moments exerted on it.
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.