Methodology of Reduced Energy/Stiffness Analysis for buckling of imperfection-sensitive shell structures

LUIS A. GODOY

Rossano

Congreso; Convegno del Gruppo Italiano di Meccanica Computazionale (GIMC); 2012

Advances in computational methods to model the nonlinear elastic behavior of shell structures have generated new computer capabilities to solve complex industrial problems. Shell buckling involves a number of specific features not present in other structural forms, such as imperfection-sensitivity, load-sensitivity, mode interaction, and exchange of energy contributions along a nonlinear equilibrium path. However, rather than using increasingly complex tools, it is also desirable to have methods in which the physics of the problem is taken into account to set theoretically loaded models, which can be solved using simpler computational tools. A strategy, known as Reduced Stiffness Method, has been developed in which selected energy components are eroded as a consequence of mode interaction and imperfection-sensitivity. This physical interpretation allows the formulation as an eigenvalue problem, in which the critical loads are lower bounds to experiments and to nonlinear incremental analysis. This paper considers the computational implementation of a reduced stiffness approach to the buckling of shell structures. The structural configurations of interest in this work are cylindrical storage tanks with a roof (either flat or conical roof), in which case the thickness is decreased from the bottom to the top of the cylindrical part. A reduced stiffness approach has been implemented in a finite element code for shells of revolution, in which stabilizing membrane components are eliminated on the assumption that they will be eroded due to imperfection-sensitivity and mode interaction. The code is employed to estimate buckling loads and modes in tanks with various roof configurations. It is shown that two aspects influence the results: first, the existence of zones with different stiffness in the structure, and second, a load with a circumferential variation. The present results are compared with geometrically nonlinear analysis including shape imperfections and with experimental results. The results indicate that a reduction in meridional and torsional membrane components applied on a zone of the shell leads to good results in terms of limit point loads and modes.