Robust nonlinear finite shell element analysis of civil engineering structures

Abstract

Finite shell elements are widely used in prediction of the structural behaviour of civil engineering structures. Over the past decades, many shell elements based on different theories and assumptions have been developed either for general or special shell structures. However, there still exists a need to develop or improve shell elements so that they can capture the critical effects of shell structures with high computational efficiency. For example, accurate and efficient shell elements for civil engineering structures such as walls, floors, roofs of buildings and thin-walled structures are urgently required to consider both the geometric and material nonlinearities. With the recently significant improvement of computer hardware, it is possible to perform nonlinear analysis and design of structures with thousands of degrees of freedom in personal computers even laptops. For building structures, it is vital to develop robust shell elements with good convergence to link to advanced beam-column elements for second-order direct analysis, so that a safer and more economical design can be achieved. Thus, this research project aims to propose high performance flat triangular and quadrilateral shell elements with advanced techniques for nonlinear finite element analysis. The assumption of large displacements, large rotations, but small strains, well accepted in geometrically nonlinear analysis and applicable to most civil engineering structures, is adopted in this study. The main contributions of this research project are summarised in the following. First, a novel pure deformational method is proposed to simplify the shell element formulations and as a result the associated quantities and the computational cost are significantly reduced. The pure deformational method has been widely utilized in the derivation of both displacement-based and force-based beam-column elements. However, the application of this technique in shell elements is not popular as beam-column elements due to increasing complexity in shell elements. Thus, narrowing the gap will make a significant contribution to the development and improvement of finite shell elements. It should be pointed out that the proposed pure deformational method has a wide application range since it is independent of the element type which may be derived with different assumptions and theories, once the element shape (triangle or quadrangle) is known. Also, the pure deformational method can contribute to a novel element-independent co-rotational (EICR) formulation, which is a well-accepted formulation for geometrically nonlinear finite element analysis. The EICR formulation is different from the traditional total Lagrangian (TL) and updated Lagrangian (UL) formulations based on the Green-Lagrangian strains. Further, the thesis proposes a novel EICR formulation for triangular and quadrilateral shell elements based on the proposed pure deformational method. In the EICR formulation, the geometrically nonlinear analysis procedure for flat quadrilateral shell elements is more complicated than the one for flat triangular shell elements, because of the warping phenomenon that the 4 corner nodes of quadrilateral shell element being not coplanar may occur during the analysis process. Thus, unlike flat triangular shell elements, the warping effect should be considered in the derivation of geometrically nonlinear quadrilateral shell elements. In addition, different from the traditional EICR formulation, the proposed EICR formulation is simpler by using pure deformational method and therefore enhances the numerical efficiency of geometrically nonlinear analysis. Based on the proposed EICR formulations, a nonlinear triangular shell element and a nonlinear quadrilateral shell element are developed. The elastoplastic behaviour of shells is considered based on the layered approach in which a shell will be divided into several layers through the thickness. The proposed elements allow for the transverse shear effect and the drilling rotations and therefore can be used to analyse various civil engineering structures. The inclusion of drilling rotation allows the shell elements to effectively connected in-plane to beam-column elements. These numerical examples show that the proposed shell elements can analyse thin shell structures without locking problems. Finally, the proposed nonlinear shell elements based on the simplified EICR method are implemented in the program NIDA. A number of benchmark problems are provided to verify the proposed shell elements. The present results compared well with other elements in commercial software and literature illustrate that the proposed nonlinear shell elements are robust, accurate and efficient.