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A Linearization Technique for the Dynamic Response of Nonlinear Continua.
Krousgrill, C. M.
National Science Foundation, Washington, DC., January 1981, 150 p.
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A technique for understanding the dynamic response of structural elements is developed. The technique is based on the concept of the equivalent linearization method which relies on obtaining an optimal linear set of equations to model the original nonlinear set. The linearization is performed at the continuum level, because the equivalent linear stiffness and damping parameters are physically realizable and are defined in such a way that the method could be easily incorporated into finite element computer codes. Three different approaches, each based on the minimization of a distinct difference between the nonlinear system and its linear replacement, are taken. Existence and uniqueness properties of the minimization solutions are established and procedures for solving the equivalent linearization are discussed. The method is applied to three specific examples: one dimensional, hysteretic shear beams; thin plates governed by nonlinear equations of motion; and the same nonlinear plates but with cutouts. Solutions via the equivalent linearization method using the stress difference minimization compares well with Galerkin's method and numerical integration. The last example is easily handled by the continuum equivalent linearization technique, whereas other methods prove to be inadequate.
Dynamic response; Theses; Numerical integration; Earthquake engineering; Linear differential equations; Nonlinear structural analysis; Computer applications; Finite element analysis; Nonlinear differential equations; Mathematical models; Structural analysis; Dynamic structural analysis