DOI: 10.26634/jce.13.4.20451 ISSN: 2231-1068

A step by step analysis to solve the equation of motion in space and time using basis splines - A class room example

K. N. V. Chandrasekhar
  • General Medicine
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The use of splines to model the geometry and perform iso-geometric analysis is fast replacing conventional finite element analysis. In this paper, the main objective is to analyze the equation of motion using basis splines. The equation of motion is a function of both space and time. The finite difference method is used to evaluate the newer values of the function at each time step. The splines are used to determine the mass matrix and the stiffness matrix. The sample code is also presented. The displacement vector at each time step is shown using graphs. The graphs clearly show how the member vibrates at each time step and the state of the beam. The analysis clearly shows how the Galerkin method can be applied with a weak formulation to solve for the displacement vector in a step-by-step method. Two problems are discussed, the first is a classroom example, and the second is a home work example, which may require a bit of effort to determine the value of the nodal displacement vector at several nodes for each time step.

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