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To analyze the plane problem with irregular mesh and complicated geometry, it is helpful to utilize the triangular element. In this study, several optimization criteria will be elaborated. By utilizing these provisions and satisfying the equilibrium conditions, a novel triangular element, named SST, is developed. To demonstrate the high accuracy and efficiency of the new element, a variety of structures will be solved. The findings will prove that the presented element has a low sensitivity to the geometric distortion. Moreover, the parasitic shear error will not arise when this element is employed. In addition to these, the proposed element is rotational invariant. Comparison studies will reveal that the SST element is more robust than the other well-known triangular ones.

Graphene sheets are the basis of nano-electromechanical switches, which offer a unique insight into the world of quantum mechanics. In this paper, we proposed a new size-dependent multi-beam shear model for investigating the pull-in instability of multilayer graphene/substrate nano-switches within the context of the Timoshenko beam theory. As the graphene/substrate bemas bent toward the graphene layer due to the thermomechanical mismatch, the impact of curvature is considered in the proposed model. Also, the impact of the Casimir attraction is incorporated in the developed model by taking into account the limited conductivity of interacting surfaces. The scale dependency of the materials is considered in the framework of the nonlocal elasticity. To simulate the nano-switch and explore the pull-in instability, a finite element procedure is developed. The proposed approach is verified by comparing the pull-in voltage to published data. Finally, the role of influential parameters, including size dependency, length, initial gap, curvature, and the number of graphene layers on instability voltage of nano-switch, are investigated.

In this paper, two efficient elements are proposed by utilizing hybrid Trefftz method for the analysis of thin plate bending. The triangular element, THT, and the quadrilateral element, QHT, which have 9 and 12 degrees of freedom, respectively. Two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a way that it satisfies the governing equation of the thin plate. Boundary field is dependent on the nodal degrees of freedom via boundary interpolation functions. For deriving boundary interpolation functions, element's edges are assumed to deform like a beam, and the related interpolation functions are used for the boundary fields. The solution accuracies of the famous and hard bench mark problems, such as circular and skew plates, prove the justification of suggested elements. Based on the various test problems, QHT in comparison to other four-sided elements, and THT in comparison to triangular ones, show better results and rapider convergence rate.

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