Stability Analysis of Composite Perforated Annular Sector Plates Under Thermomechanical Loading by Finite Element Method

Abstract

This paper presents the stability analysis of a perforated plate with sector geometry made of composite materials. The sector of concern is a compound of graphite-epoxy and glass-epoxy with identical ply thickness but different fiber angles for each layer. The mechanical load conditions considered include uniform axial, circumferential, and biaxial pressure, while the thermal loading is specified to be uniform temperature increase over the whole sector. The existence of one or two circular holes has increased the complexity of analysis. To obtain solutions of high accuracy, the three-dimensional elasticity theory relations have been employed. Using the finite element method along with the stability condition of Trefftz, the buckling equation of the structure is derived. Green nonlinear strain-displacement relations are used to form the geometrical stiffness matrix. Unlike the finite element method used by other researches, a novel curved 3D B-Splined element is used to more accurately trace the displacement and stress variations of the structure. This element can be used in solution domains with geometric discontinuities, such as perforated plates and also meshed in the thickness direction. Moreover, instead of using the common von Karman assumptions, the most general form of the strain tensors in the curvilinear coordinates is adopted. The buckling load is obtained by extremizing the second variations of the total potential energy. The finite element formulation is coded in the MATLAB software. The effects of various parameters such as sector dimensions, dimensions of the hole, mechanical load directions, and fiber angles of each layer on the thermomechanical buckling is investigated.

Badanie Wpływu Zamocowania Kołowej Płyty Perforowanej Na Koncentrację Naprężenia W Warunkach Działania Ciśnienia Hydrostatycznego

“…Spośród nich należy wymienić następujące: wyznaczanie koncen-tracji naprężenia, rozkładu ugięcia, stanu odkształcenia, wartości współczynnika koncentracji oraz intensywności naprężenia w płytach perforowanych osłabionych otworami [1][2][3][4][5][6][7][8]. Do oceny zachowania płyt perforowanych pod obciążeniem stosuje się metody: analityczną [2,4,5,9,10], doświadczalną [11,12] oraz numeryczną [13][14][15][16][17][18][19]. Wykorzystuje się również nowe podejście za pomocą metod numerycznych opierających się na metodzie elementów skończonych (MES).…”

Thermoelastic Coupling Vibration and Stability Analysis of Rotating Annular Sector Plates

“…Considering that the varying temperature along the radial direction is ignored, the following equation is derived by using (9) and (16).…”

“…Behzad et al [15] used 3D elasticity theory to analyze the thermal buckling of functionally graded perforated annular sector plates. Shaterzadeh et al [16] used the finite element method to discuss the stability of composite perforated annular sector plates under thermomechanical loading. Mirtalaie [17] studied free vibration of functionally graded sector plates in thermal environment and examined the effects of temperature field, volume fraction exponent, radius ratio, and sector angle on free vibrations of the sector plate.…”

“…The differential equation of thermoelastic coupling transverse vibration of the rotating annular sector plate is the fourth-order partial differential equation with variable coefficients. The high-order partial differential equation has been solved by the finite element method and Galerkin method in some literature [13,16,[18][19][20]. The differential quadrature method (DQM) was firstly proposed by Bellman and Casti in early 1970s [21].…”

Finite-difference analysis of stresses of a non-uniform functionally graded material circular disk rotating in the magneto-thermal environment: An equal mass study

“…Leu and Chien 25 implemented the FE formulation for FGM disk with variable thickness under the non-uniformly distributed heat source and power-law distribution of material properties. FE analysis of a composite plate with sector geometry under thermomechanical loading is shown by Shaterzadeh et al 26 They studied the response of a plate sector with one or two holes subjected to a uniform temperature rise in the presence of compressive mechanical loading in axial, circumferential, and biaxial directions. Hassani et al 27 followed three different approaches, namely, variable material properties (VMP), Runge-Kutta's (RK), and FE method (FEM), to solve the thermo-elastic problems of an FGM rotating disk with variable thickness; the correspondence among these solutions are also analyzed in the study.…”