| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 97 === This study presents the analyses of highly nonlinear planer frame structures using the theory of vector form analysis. Including nonlinear geometry, material, contact/impact and fragment properties, rathen than treating three nonlinear properties such as geometry, material, contact/impact and fragment via analytical mechanics, vector form analysis is developed based on vecter mechanics. The structure is firstly described by a set of particles. The period of analysis are modeled via a set of discrete path element. The interactions among particles are complemented by the generalized forces evaluated by vector form intrinsic finite element (VFIFE). The governing equations, derived via Newton’s law are sloved by finite difference method. It is convenient to update the reference frame and change the constrain conditions.
A bilinear elastic-plastic material model with mixed hardening rule and Cowper- Symonds equation for strain rate sensitive material is adopted to account for the material nonlinearity. The contact algorithm includes contact search and penalty function method. The fragment behavior is dealt by fragment criterion.Finally, a few numerical examples are presented to demonstrate the validity of vector form analysis.
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