The Effect of Equilibrium Equation and Trefftz Functions on the Responses of Quadrilateral Bending Plate

Document Type : Original Article

Authors

• Mohammad Rezaiee Pazhand ¹
• M. Malekzadeh ²
• N. Razbzadeh ²

¹ Ferdowsi University of Mashhad

² Ferdowsi

10.22067/fum-mech.v29i2.50733

Abstract

In this study, ten novel quadrilateral Kirchhoff’s bending plate elements based on the Trefftz displacement functions and satisfying equilibrium equation are suggested. First, the most suitable arrangement of degrees of freedom and nodes are achieved by benefiting from previous researches. Afterwards, using the symmetry of terms, ten elements with different interpolation functions for the two top arrangements will be introduced. Numerical tests reveal that the correct choice of the interpolation’s terms from the incomplete Trefftz functions leads to more efficient elements with lower degrees of freedom and higher order than the complete elements. Since the Trefftz functions meet the equilibrium conditions, the force responses of the most cases have a higher accuracy than the displacement responses.

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Keywords

• Thin bending plate
• equilibrium equation
• Analytical Solution
• Trefftz function
• quadrilateral bending element
• incomplete interpolation function

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