A three-node triangular element with continuous nodal stress

• A 3-node element with continuous nodal stress (Trig3-CNS) is presented.
• The shape functions of Trig3-CNS are C1 continuous at nodes.
• Trig3-CNS is able to obtain nodal stress without any smoothing operation.
• Comparing to 3-node element, the Trig3-CNS has high tolerance to mesh distortion.

A three-node triangular element with continuous nodal stress (Trig3-CNS) is presented. The present work is the development of the partition-of-unity based ‘FE-Meshless’ quadrilateral element with continuous nodal stress (Quad4-CNS). This triangular element, Trig3-CNS, is potential to replace Quad4-CNS when the geometry of computational domain is too complex to generate quadrilateral meshes. The three-node triangular element (Trig3) is widely used, however it is always of low accuracy due to its low order of trial functions. By increasing the order of trial functions, Trig3-CNS obtains better accuracy and higher convergence rate as compared to Trig3. The numerical tests in this paper demonstrate that Trig3-CNS has higher tolerance to mesh distortion as compared to the Trig3 and four-node quadrilateral element (Quad4). Another advantage is that the derivative of Trig3-CNS shape function is continuous at nodes, therefore Trig3-CNS is capable of giving smoother solution and calculating nodal stress without any extra smoothing operation.