Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells

Abstract

DOI: 10.2514/1.J051003Theprojectionoftheequationsofmotiononasuitablemodalbasiscandrasticallyreducethenumberofdegreesoffreedom of a nonlinear dynamic !nite element analysis. A reduction method based on enriching a set of vibrationmodeswithsecond-ordermodescalculatedviaaperturbationtechniqueispresented.Thesesecond-ordermodesarereadily calculated via the solution of corresponding linear problems. The results indicate that the second-ordermodes are displacement !elds that are essential for an appropriate representation of the nonlinear behavior of thestructure. Problems exhibiting strong geometrical nonlinearities under relatively high dynamic loads aresuccessfully handled by forming the reduction basis with vibration modes and their corresponding second-ordermodes, calculated at two different static equilibrium con!gurations.