STATIC ANALYSIS OF A COMPOSITE I-BEAM USING THE RAYLEIGH-RITZ AND PENALTY FUNCTION METHODS

摘要

Design optimization of a composite I-beam requires an efficient stress analysis method, as thernlatter will typically be executed thousands of times. Although the mechanics of laminated beamsrn(MLB) offers such efficiency, its assumptions about strain in the beam cross-section mean thatrnshear and axial stresses are predicted to be constant in vertical and horizontal walls respectively.rnThis is an inaccurate representation of the true stress field, particularly in the shear web wherernlateral stress variations can be significant. Furthermore, MLB fails to account for the effects ofrnwarping. Although the finite element (FE) method is capable of predicting these behaviors, thernrequired pre- and post-processing is generally time consuming. Furthermore, point loads andrnpoint supports require fine meshes that quickly become computationally expensive. In this paper,rnwe suggest an alternative, semi-analytical approach that accurately captures both lateral stressrnvariations and warping, yet provides comparable computational efficiency to MLB.