on 27-Dec-2019 (Fri)

My objective in this set of lectures is to introduce to you finite element methods for the linear analysis of solids and structures. ["Iinear" meaning infinitesimally small displacements and linear elastic material properties (Hooke's law applies)]

The finite element solution process can be described as given on this viewgraph. You can see here that we talk about a physical problem. We want to analyze an actual physical problem. And our first step, of course, is to establish a finite element model of that physical problem. Then, in the next step, we solve that model. And then we have to interpret the results. Because the interpretation of the results depends very much on how we established the finite element model, what kind of model we used, and so on. And in establishing the finite element model, we have to be aware of what kinds of elements, techniques, and so on are available to us. Well, therefore, I will be talking, in the set of lectures, about these three steps basically here for different kinds of physical problems. Once we have interpreted the results we might go back from down here to there to revise or refine our model and go through this process again until we feel that our model has been an adequate one for the solution of the physical problem of interest.

The analysis of an engineering system requires:

• idealization of system
• formulation of equilibrium equations
• solution of equations
• interpretation of results

The analysis of a complex continuous system requires the solution of the differential equations using numerical procedures. And this solution via numerical procedures really reduces a continuous system to a discrete form. The powerful mechanism that we talk about here is the finite element method implemented on a digital computer.

Steps involved in the analysis of discrete systems:

• system idealization into elements
• evaluation of element equilibrium requirements
• element assemblage
• solution of response

Because many of the characteristics that we are using in the analysis of discrete systems, discrete meaning, springs, dashpots, et cetera, we can directly see the discrete elements of the system. The steps involved in the analysis of such discrete systems are very similar to the analysis of complex finite element systems. The steps involved are the system idealization into elements. And that idealization is somewhat obvious because we have the discrete elements already. The evaluation of the element equilibrium requirements, the element assemblage, and the solution of the response. Notice when we later on talk about the analysis of continuous systems instead of discrete systems, then the system idealization into finite elements here is not an obvious step and needs much attention. But these three steps here are the same in the finite element analysis of a continuous system.

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