# Advanced Structural Analysis/Part I - Theory

# Introduction edit

The theory of applied structural analysis is extensive. Clearly it entails a vast amount of mathematics and physics, but it should also put forth some other aspects that cannot always be treated in the same precise manner. Such aspects may be: sound working patterns, the concept of safety, conservative design etc. This part of Advanced Structural Analysis is an ambitious ongoing attempt to thoroughly cover the wide range of topics schematically outlined above.

The topics of this part of the book follow in a rational order of progressing insight into the theory of structural analysis. At the starting point, *Philosophy of Structural Analysis*, we enter a place where nothing is known about solid mechanics except that mechanical structures sometimes fail to work as desired. The discussion is very general, and establishes fundamental view-points that naturally lead towards an exploration of engineering materials.

In *Materials*, basic concepts such as elasticity, plasticity etc. are explained as thoroughly as possible without extensive use of mathematics. Eventually, the discussion reaches a point where a more sophisticated mathematical approach is needed in order to deepen our understanding of the general behavior of solid materials. We then resort to *Continuum Mechanics*.

*Continuum Mechanics* is a powerful mathematical machinery that describes the mechanical behavior of continua, i.e. continuous deformable material volumes. It provides insights that are essential to the theoretical treatment of elasticity, plasticity, fatigue, FEA, etc. and is key in practical structural analysis.

*Residual Stress*, follows next. The chapter explains the concept of residual stress, and outlines common causes and the effects it may have on mechanical structures.

We have now covered the prerequisites of the next chapter, *Failure Modes*. Here the previous sections come together and pave the road to in-depth understanding the different failure modes that may occur in a structure.

**Constraints and Loads..**

We are now ready to discuss *Optimization*. Different optimization methods and goals are covered extensively.

At this point we have acquired a substantial body of theoretical knowledge, and the ability to understand the nuances of structural integrity and functioning. Therefore, it is time to move on to a more formal context where legal documents regulate specifics of how the analysis of engineering products should be conducted. *Normative Documents* covers these regulations, continent by continent, and is a springboard into these matters.

Previous chapters have established a fairly good idea of what questions need to be asked before and during a structural analysis. Now we find out how to get the answers. *Modeling* covers major topics such as analytical methods and FEA.

Equipped with the knowledge of how to perform advanced analysis of engineering products, we need to discuss ways to control the quality of our work. There are many possible sources of error, including: data input errors, modeling assumptions that may be incorrect, numerical problems, software bugs etc. Due to the complexity of most analysis tasks, it is important to have routines and strategies for sifting the errors out of the solution. *Verification and Work Flow* provides suggestions for how to eliminate significant errors from you analysis.

The last chapter, *Analysis Documentation*, of this part of the book outlines important features of the analysis documentation.