Book Description

This text is designed for those who already know structural calculation. It starts with the simple exercise of reformulating the direct stiffness method using matrices. The aim is to allow the student to understand the enormous power and generality of the weak formulation for the approximation of strut structure problems by using a formulation which is easy to understand. The correspondence of results of the initial classical formulation with those of the FEM when using linear shape functions and Hermite polynomials allows us to tackle the general formulation of the fundamental concepts of the method more easily. Once the method and the details of its general formulation are understood (although only through its application in a specific structural type), the FEM is presented in a general way, as a procedure for obtaining approximated solutions for partial differential equations. The approaches to field problems and to linear elasticity problems are presented as examples. The method has been now clearly presented and therefore, the selection of the type of element, with the generation of interpolation functions of higher degree and their systematization in element families, can be studied in greater depth. This part finishes with the introduction of the idea of isoparametric transformation that, together with numerical integration, explains the stage of development reached by the method. Finally, the subject relative to plates is dealt with, looking at their specific use as structural elements, and trying to show the difficulty of satisfying the continuity between elements in thin plates, and the shear locking solution in thick plates amongst other things