Determination of Forces and Moments Per Unit Length in Symmetric Exponential FG Plates with a Quasi-Triangular Hole

Abstract

In this study, the resultant forces and moments acting on infinite symmetric FGPs with a triangular hole subject to uniaxial tensile load were examined via an analytical method using the complex variable approach. The mechanical properties of graded plates are hypothesized to vary throughout the thickness exponentially. The impact of various factors, namely hole orientation, hole aspect ratio as well as the hole corner curve on stress distribution and moment resultants is considered. In order to approve the credibility of the analytical approach, its outcomes are compared to numerical results acquired from ABAQUS finite element modeling. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes. Based on these results, the mentioned factors entail a considerable effect on the distribution of resultant forces and moments at the proximity of the hole and the load bearing tolerance of functional grated plates with holes may be enhanced by suitable selection of the aforementioned parameters.

Cross-Sectional Performance of Hollow Square Prisms with Rounded Edges

“…In addition, the model is essentially different from super-ellipses [14,15], being expressed in terms of the p-norm and the vector notation by r − r 0 p = const, or its generalization called a Gielis curve [16][17][18], while both of them are known as powerful tools for describing the natural shape of plants. Furthermore, a method of drawing a rounded triangle by using a complex function has been proposed quite recently [19], but again, our method is essentially different from it.…”

Mutual Influence of Geometric Parameters and Mechanical Properties on Thermal Stresses in Composite Laminated Plates with Rectangular Holes

“…The plane stress components using Equations (5) and (6) in the stress function are given as Equation 7:…”

“…In recent decades, the increasing requirements for the improved performance of structures has made designers interested in designing structural elements with optimal shapes [3,4]. Different shapes of holes in the structures are required to minimize the structures' weight and supply accessibility other than the system parts [5,6]. In most cases, the hole is not created at the beginning of the initial design [7].…”

Stress concentrations in skew pressurized holes: A numerical analysis

“…The effects have been studied for cases involving equally and variably pressurized holes as well as holes subjected to uniaxial and biaxial stresses. Other related cases which have been considered in literature [25], involve the effect of hole shape (in cases of elliptical [26] or polygonal holes [27][28][29]) on the stress distribution mapping of the system, the influence of reinforcement on the periphery of the hole [30], periodically-replicated hole arrangements [31,32] and coalesced holes [33], as well as holes subjected to thermoelastic [34,35] and external stress loading [36,37]. These problems have been tackled using a variety of analytical and numerical methods which have yielded both exact and approximate solutions, with varying degrees of complexity and mathematical robustness.…”