On the Accuracy and Convergence of the Hybrid FE-meshfree Q4-CNS Element in Surface Fitting Problems

Tjong, Wong Foek and SOETANTO, RICHO MICHAEL and Budiman, Januar (2017) On the Accuracy and Convergence of the Hybrid FE-meshfree Q4-CNS Element in Surface Fitting Problems. In: The Third International Conference on Sustainable Infrastructure and Built Environment, 27-09-2017 - 27-09-2017, Bandung - Indonesia.

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Abstract

In the last decade, several hybrid methods combining the finite element and meshfree methods have been proposed for solving elasticity problems. Among these methods, a novel quadrilateral four-node element with continuous nodal stress (Q4-CNS) is of our interest. In this method, the shape functions are constructed using the combination of the ‘non-conforming’ shape functions for the Kirchhoff’s plate rectangular element and the shape functions obtained using an orthonormalized and constrained least-squares method. The key advantage of the Q4-CNS element is that it provides the continuity of the gradients at the element nodes so that the global gradient fields are smooth and highly accurate. This paper presents a numerical study on the accuracy and convergence of the Q4-CNS interpolation and its gradients in surface fitting problems. Several functions of two variables were employed to examine the accuracy and convergence. Furthermore, the consistency property of the Q4-CNS interpolation was also examined. The results show that the Q4-CNS interpolation possess a bi-linier order of consistency even in a distorted mesh. The Q4-CNS gives highly accurate surface fittings and possess excellent convergence characteristics. The accuracy and convergence rates are better than those of the standard Q4 element.

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