A FINITE ELEMENT APPROACH TO UPPER BOUND SOLUTIONS FOR ULTIMATE LOADS OF PLATES AND SLABS

Resumo

Structural engineering projects involves the elements design considering the ultimate limit
state (ULS) conditions and the service limit state (SLS) check. The ULS is characterized by the
exhaustion of the strength capacity of the entire structure or some specific regions. SLS conditions
should be checked to ensure durability of the structure, maintenance of non-structural elements
appearance and integrity, which influence users comfort as well as the buildings functionality. No
additional loading can be sustained by the structure beyond the ultimate state conditions. The present
work aims at analyzing the ULS of plates and slabs under predominating flexion through numerical
evaluation of their load capacities. The combination of the kinematic approach of limit analysis theory
(LAT) with the finite element method (FEM) enabled the development of a computational tool that
allows for assessing the failure load of plates and slabs with arbitrarily geometry and associated
support conditions when subjected to different loading modes (surface, linear and concentrated).
Adopting the normal deflection rate as main variable that controls the failure mechanism, six-node
triangular finite elements were used for geometry and kinematics discretization. The numerical
determination of ultimate load of the structure relies upon a minimization procedure. The latter is
achieved by Sequential Quadratic Programming (SQP) method, which is an iterative method for
constrained nonlinear optimization. The developed finite element tool also allows the analysis of the

failure mechanism of plates and slabs and visualization through the software of pre-and post-
processing GiD®. For the validation of the proposed analysis methodology (LAT + FEM) and

associated computational implementation, analytical results of various slab and plate configurations
and their respective rupture mechanisms were favorably compared with the numerical predictions.
Comparison with available approaches are also presented, thus indicating the ability of the developed
numerical tool to accurately assess the ultimate loads and failure mechanisms of bending plates or
slabs.