STRUCTURAL ANALYSIS

Structural analysis is intended to arrive at stresses, strains and deformations of a structural component or structural system subjected to different types of loads and loading conditions.  Efficient and reliable methods  of structural analysis have to be used to arrive at safe and economical designs of large and complex structures such as multistoreyed buildings long span bridges, shell structures, etc. It is well recognized that the Finite Element Method (FEM) can be used to solve almost all types of structural analysis problems. The accuracy and reliability of the solution depends on how well the real structure and the problem are modeled for FE analysis, which in turn depends on the understanding of the basis and limitations of the FEM  and the chosen software.

Finite Element Modelling for Structural Analysis

The first step in FE analysis is to model/idealise the geometry of the structure for the particular requirements/goals of the structural analysis on hand. For example, in the preliminary design stage, a one dimensional model of the structure (say a tall building) may be adequate for determination of natural frequencies and mode shapes while in the final design stage, one may have a 3-D model of the structure for evaluation of natural frequencies and mode shapes to determine its seismic response accurately. That is, the model will be different for different purposes or stages of analysis and design. Related consideration to this modelling is whether this process can be automated. The geometry of the real structure/component is the starting point for development of a geometrical model for finite element analysis. Transforming the geometry of the real structure into the geometrical model for finite element analysis is a complex process in which engineering knowledge and expertise relating to various aspects of structural behaviour/analysis, computer software and hardware facilities and their limitations have to be considered. It may be noted that large amount of data and its manipulation will be involved in this process. Advances have been made to develop methodologies and expert systems in this area to facilitate automatic/integrated modelling for FE analysis.

In the next stage of analysis process, the finite elements to be used and the meshing pattern (including size) of the FE model and the boundary conditions are to be decided/modelled. It may be mentioned here that the mesh pattern and size is very much dependent on the actual finite elements chosen for the particular structure, loading and behaviour to be analysed.  In this context, the finite element is meant to indicate the type of element (including the number of degrees of freedom) and the material model to take into account different types of behaviour such as isotopic, orthotropic, elastic, elasto-plastic, etc. For analysis of vibration and dynamic response, modelling/representation of mass has a significant influence on the accuracy of results. Although the effect of damping is not generally considered for free vibration analysis, damping effects have to be modelled suitably in the dynamic responses. While accurate representation of damping is a complex problem 1% of critical damping is normally used in the dynamic response analysis.

Another important aspect of modelling which has significant influence on the results of analysis is modelling of realistic loading - static, dynamic, including transient phenomena, random, etc. - on the structure. It may be emphasised here that considerable engineering knowledge and judgement has to be used to arrive at good approximations to the actual response of the structure by employing simple models to represent the materials, structural behaviour and the actual loading. Significant advances have been made recently in modelling of steel reinforced concrete structures to understand their behaviour upto ultimate failure taking into account the material and geometric nonlinearities. The phase of setting up the equilibrium equations (in the case of displacement based Finite Element analysis) and seeking the solution involves the use of different algorithms (or numerical analysis models). The efficiency of the algorithms used is a matter of considerable importance in the analysis of large size problems and particularly dynamic and non-linear analysis.

It may be noted that the considerations of modelling of different aspects in the structural analysis process are highly interdependent. Currently, vigorous efforts are being made to formulate methodologies, to study the errors in analysis results due to modelling schemes, and to formulate approaches for adaptive refinement of models to achieve solution accuracies to the desired levels. These include strategies with mesh refinement (h-adaptive) and using hierarchical finite elements (p-adaptive). Significant contributions are being made over the last decade in the field of stochastic finite element analysis including structural dynamics considering parametric uncertainties. Advances are also being made in the development and application of parallel processing algorithms and strategies to solve large and complex problems of structural analysis. Knowledge-based expert systems also being developed to help the analyst in FE modelling and also with the aim of automating the analysis process. Generation of a finite element mesh modelling the geometry of the structure is an important step in finite element structural analysis. Advances are being made towards automating the mesh generation and in making use of advanced visualisation/graphical features in order to facilitate and save time in generating finite element meshes for structures of complex geometry. Development and use of Graphic User Interface (GUI) for pre-processing of input data for finite element analysis is the present trend.