NUMERICAL TECHNIQUES IN PROBLEM-SOLVING

Have you ever thought what is that most essential thing used for designing in Mechanical Engineering? Well, to every designing concept and preparation analyzing plays an essential role. To analyze a complex problem of interest, for example, stress analysis the techniques can be classified into Analytical, Numerical and Experimental. Though the Analytical solutions offer a closed-form solution but it is limited to only few problems because of the geometry and shape constraints. However, performing experiments for every problem is not possible due to cost and other constraints.

In this regard, numerical techniques have played a vital role in solving the problems at hand over the last few decades. Since, it involves the solving of a large number of complex higher-order differential equations.

With the advent of high processing capabilities of modern computers, these techniques have gained more popularity and referred to as computational techniques are used in recent times for solving a wide variety of problems in sectors of manufacturing and designing. The three most common numerical methods employed are finite difference, finite element and boundary element methods. Considering the problems, FEM is the only method used for solving it. After several experiments and studies it was found that approximately 500 commercial software are used for working with this method.

Want to know more about this innovative technique, then you need to get deep into this article.  The whole technique works on the principle based on the divide and conquers. The geometry of the component in FEM analysis is to divide into several elements and nodes thus reducing infinite degrees of freedom to finite. At first, the physical problem on hand is converted to a mathematical model through governing differential equations based on certain assumptions related to geometry, kinematics, material laws, loading parameters, boundary conditions and more.

There are infinite element solutions in mathematical model that involves the choice of elements, mesh density, solution parameters and representation of loading conditions. In order to predict the accurate response of the system one has to revisit the solution parameters and refine the mesh iteratively.

For example:- To perform stress or deformation analysis in commercial FEM-based software like ANSYS following steps are required.

a. Building a model

b. Defining element type (2D spar, beam etc.)

c. Defining element real constants (area, a moment of inertia, etc.)

d. Defining material properties (linear/nonlinear, isotropic/anisotropic, temperature-dependent etc.)

e. Applying the load (constrained, supports, specifying boundary condition etc.)

f. Obtaining the solution (maximum stresses, deflection etc.)

Apart from structure, it finds its applications in other domains too, like thermal and fluid flow, Electromagnetic field, Biomathematics, Geo Mechanics, electrical network analysis, electromagnetic, and insulation design analysis in high-voltage equipment, dynamic analysis of motors and heat analysis in electrical and electronic equipment’s. Though the techniques, unlike analytical methods provide approximate solutions but with the refinement in techniques on day to day basis these are now capable of reasonably solving a large variety of real-time industrial problems.

CONNECTION OF FEA WITH SISTec

Well, the research and development section of Mechanical Engineering is completed related to FEA. The Training and Knowledge in B. Tech level students should match with the industrial requirements. However, keeping in mind major and minor requirements of Industry, SISTec – Department of Mechanical Engineering makes sure that it appoints faculties who have possessed the relevant knowledge over the subject. They should be capable of guiding students in B Tech. and M.Tech, undertaking projects related to real-time industrial problems.

Apart from subject knowledge Sagar Group of Institutions – SISTec many value-added programs in the form of modules based on various skills are also run throughout the academic year to bridge the gap between academia and industry.

Written By:

Dr. Sanjay Kumar Singh
Professor, Department of Mechanical Engineering
SISTec, Bhopal