2014/5/15 ustries,and even students rimary unknowns Pre-processing Fun What is this class about? Physical model FEA model Physical model FEA model FEA theory Results FEA theory Poat-processing Fun! FEA core Math!! 3 2014/5/15 3 Comparison of the computed axial stress value in a tapered cylinder.  In the FEM, a complex region defining a continuum is discretized into simple geometric shapes called elements.  The properties and the governing relationships are assumed over these elements and expressed mathematically in terms of unknown values at specific points in the elements called nodes.  An assembly process is used to link the individual elements to the given system. When the effects of loads and boundary conditions are considered, a set of linear or nonlinear algebraic equations is usually obtained.  Solution of these equations gives the approximate behavior of the continuum or system.  The continuum has an infinite number of degrees-of-freedom (DOF), while the discretized model has a finite number of DOF. This is the origin of the name, finite element method.  The number of equations is usually rather large for most real￾world applications of the FEM, and requires the computational power of the digital computer. The FEM has little practical value if the digital computer were not available.  Advances in and ready availability of computers and software has brought the FEM within reach of engineers working in small industries, and even students. Two features of the finite element method are worth noting.  The piecewise approximation of the physical field (continuum) on finite elements provides good precision even with simple approximating functions. Simply increasing the number of elements can achieve increasing precision.  The locality of the approximation leads to sparse equation systems for a discretized problem. This helps to ease the solution of problems having very large numbers of nodal unknowns. It is not uncommon today to solve systems containing a million primary unknowns