Teaching Finite Element Analysis As A Solution Method For Truss Problems In Statics

Finite Element Analysis (FEA) is a very powerful tool that is used in virtually every area in the field of Mechanical Engineering and many other disciplines.It is beneficial for the mechanical engineering students to have exposure to this tool as early as possible and as frequently as possible in their engineering education.The earliest time comes when they are taught the truss problems in Statics.The FEA can be introduced as a solution method for the truss problems in Statics, without the need to involve additional knowledge of the deformation theory.This paper presents the step by step FEA formulation of the equations to solve for the forces inside the truss members and the reaction forces at the fixed and sliding joints, and compares the FEA formulation with the conventional approach closely.The students will clearly see the methodology and the essential features of FEA.Only truss member internal forces are involved in the elemental formulation and thus there is no need to introduce deformation theory.A MATLAB program is written to implement this FEA solution method.The property of the final assembled coefficient matrix, with the boundary conditions applied, determines the problem at hand to be statically determinate or statically indeterminate.In the former case, the students can easily solve for the joint forces using matrix manipulation just as in the conventional solution method.In the later case, the students are then encouraged to revisit this problem after they learn the deformation theory in the mechanics of materials course.The students are reminded that, with the introduced FEA formulation procedure deep in mind, the only major difference would be in the elemental formulation to apply FEA in mechanics of materials as well as in heat transfer, fluid mechanics, etc. FEA can then be reintroduced in these courses to strengthen the students' understanding of the basic FEA procedure and commercial FEA software can also be involved.