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| A DDA based complete and high order polynomial displacement approximation method in elastic mechanics and its cases verification |
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Abstract According to Weierstrass theorem for polynomial approximation, and based on elastic mechanics derivation where the complete and high order polynomial displacement function used in traditional DDA is employed, a DDA based complete and high order polynomial function approximation method is presented in this paper. In the method mentioned above, the complete and high order polynomial function is used as displacement function of the elastic domain, the coefficients of the basic functions of coordinate variables in polynomial are used as unknowns, and the simplex integration method is used as the analytic integration, and the simultaneous equations are established and solved in order to approach the elastic solution. Based on the study of the calculating process for simplex integration, a diagram interpretation in three-dimensional condition is presented, which is helpful to illustrate the logical relationship among the variables in the simplex integration formula and the whole calculation process for integration in a given tetrahedron. At the end of this paper, the corresponding calculation code is developed and two calculation cases, one is a three-dimensional simply supported beam with uniform loading while the other is a boundary fixed elastic plate with point loading, verify the feasibility of this method. It can be indicated by the calculation result that, with the increase of the order of polynomial function, the result of polynomial function calculated by this numerical method approximate the analytical solution monotonously. According to the polynomial approximation function with six-order in this paper, the error of displacement for simply supported beam is less than 0.2%, while the error of displacement for elastic plate is less than 0.91%. In addition, in two cases, the displacement difference, compared to the analytical solution, is within micrometer.
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Received: 10 January 2013
Published: 28 June 2014
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2014, Vol. 35 
