Element-Size Independent, Elasto-Plastic Damage Analysis of Framed Structures.

Abstract

The adaptively shifted integration (ASI) technique and continuum damage mechanics are applied to the nonlinear finite element analysis of framed structures modeled by cubic Bernoulli-Euler beam elements. A new form of evolution equation of damage, which is a function of plastic relative rotational angles, is introduced in order to remove the mesh-dependence caused by the strain-dependence of damage. The elasto-plastic damage behavior of framed structures can be accurately and efficiently predicted by the combination of the ASI technique and the new damage evolution equation. Some numerical studies are carried out to show the mesh-independence of the proposed computational method. presented the formulation for the damage analysis of RC frames by the lumped dissipation model and implemented it in the commercial finite element program. Florez-Lopez (10) gave a unified formulation for the damage analysis of steel and RC frame members. Inglessis et al. (13,14), and Febres et al. (16) conducted the analysis of steel frames considering damage and local buckling in tubular members. Addessi and Ciampi (18) proposed a new beam finite element based on damage mechanics and plasticity to analyze the cyclic structural response of plane frames. However, no discussion has been made for the mesh-dependence of the finite element solutions for the damage problem of framed structures in the existing literatures (6-18). The cubic beam element based on Bernoulli-Euler hypothesis is generally used in the finite element analysis of framed structures neglecting the effect of shear deformation (19). Toi (20) derived the relation between the location of a numerical integration point and the position of occurrence of a plastic hinge in the element, considering the equivalence condition for the strain energy approximations of the finite element and the computational discontinuum mechanics model composed of rigid bars and connection springs. The computational method identified as the adaptively shifted integration technique (21) (abbreviated to the ASI technique) was developed, based on this equivalence condition. The ASI technique, in which the plastic hinge can be formed at the exact position by adaptively shifting the position of a numerical integration point, gives accurate elasto-plastic solutions even by the modeling with the minimum number of elements. The ASI technique has been applied to the static and dynamic plastic collapse analysis of framed structures (21-24), through which the validity of the method has been demonstrated with respect to the computational efficiency and accuracy. In the present study, a new computational method is formulated for the elasto-plastic damage analysis of framed structures, based on the ASI technique for the cubic Bernoulli-Euler beam element and the concept of CDM. The non-layered approach, in which the stress-strain relation is expressed in terms of the resultant stresses and the corresponding generalized strains, is employed in order to reduce the computing time for the large-scale framed structures. A new form of damage evolution equation, which is expressed in terms of the plastic relative rotational angles and the effective element length instead of the plastic curvature changes, is proposed in order to remove the mesh-dependence of solutions in the damage analysis. The present method is applicable to the collapse analysis of framed structures including elasto-plasticity, damage initiation, its evolution and fracture. Numerical studies for simple frames are conducted to show accuracy, efficiency and the mesh-independence of the proposed method.