Process based on the Direct Stiffness Method for effecting second-order analyses of plane frames structures having elements with variable rigidity
Iara Souza Ribeiro1; Francisco Célio de Araújo1; Kátia Inácio da Silva1
1 Universidade Federal de Ouro Preto
doi:10.20906/CPS/CILAMCE2017-0321
Resumo
This paper presents a strategy based on the Direct Stiffness Method (DSM) for carrying out geometrically non-linear analyses of plane frame structures. The strategy includes special options to model elements with arbitrary cross-sections and generic variation of rigidity along their axes. Herein, all the necessary geometrical properties are calculated based on their corresponding boundary-integral representations. And this considerably alleviates the modeling of elements with complex geometrical description. To determine the elastic and geometric stiffness matrices, the principle of virtual work (PVW) is applied. A system of compatibilty equations is then generated, from which all of the coefficients of these matrices are obtained. As generic variation of rigidity is assumed, a numerical Gauss-Legendre quadrature is needed state the compatibilty equations. Several types of variation of the rigidity along the element axis are available. Concerning the nonlinear analysis, one considers a standard incremental-iterative Newton-Raphson method. In it, a co-rotational approach that allows analyzing structures under large displacements is incorporated. The validation/performance of the computational code developed has been carried out by referring to results obtained employing the SAP2000.
Palavras-chave: Direct Stiffness Method (DSM); second-order analysis; co-rotational referential; elements with arbitrary cross-sections; generic variation of rigidity along the element; 2D frameworks