Statics and Influence Functions From a Modern Perspective

Introducing Green's first and second identity as the core theorems of statics and mechanics. Formulation of the variational and energy principles of mechanics with an emphasis on the computational aspects and on the qualitative features of variational solutions.
· Derivation of influence functions from duality principles, the distinction between weak and strong influence functions, the difference between monopoles and dipoles and how amputated dipoles lead to singularities, and how singularities on the boundary pollute the solution inside the domain - an unavoidable effect in 2-D and 3-D.
· A detailed discussion of the various features of the finite element method and the key role of the notion of "shake-equivalence" as originally introduced by Turner et alt. Establishing that in linear finite element analysis the accuracy depends on the accuracy of the influence functions. Introducing Betti extended as a core theorem of finite element analysis.
· A systematic treatment of the role which Green's functions play in reanalysis, sensitivity analysis, parameter identification and in optimization. Explaining why averaging material parameters succeeds and how local stiffness changes can be identified with the action of equilibrium forces f+.
· Presenting a new technique, one-click reanalysis, which allows to make modifications to a structure by clicking on single elements and seeing directly the new shape, bypassing the need to solve the modified system.


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