Nonlinear Buckling of Fixed Functionally Graded Material Arches Under a Locally Uniformly Distributed Radial Load

Functionally graded material (FGM) arches may be subjected to a locally radial load and have different material distributions leading to different nonlinear in-plane buckling behavior. Little studies is presented about effects of the type of material distributions on the nonlinear in-plane buckling of FGM arches under a locally radial load in the literature insofar. This paper focuses on investigating the nonlinear in-plane buckling behavior of fixed FGM arches under a locally uniformly distributed radial load and incorporating effects of the type of material distributions. New theoretical solutions for the limit point buckling load and bifurcation buckling loads and nonlinear equilibrium path of the fixed FGM arches under a locally uniformly distributed radial load that are subjected to three different types of material distributions are derived. The comparisons between theoretical and ANSYS results indicate that the theoretical solutions are accurate. In addition, the critical modified geometric slendernesses of FGM arches related to the switches of buckling modes are also derived. It is found that the type of material distributions of the fixed FGM arches affects the limit point buckling loads and bifurcation buckling loads as well as the nonlinear equilibrium path significantly. It is also found that the limit point buckling load and bifurcation buckling load increase with an increase of the modified geometric slenderness, the localized parameter and the proportional coefficient of homogeneous ceramic layer as well as a decrease of the power-law index p of material distributions of the FGM arches.

Torsional Buckling of Functionally Graded Multilayer Graphene Nanoplatelet-Reinforced Cylindrical Shells

Exact solutions for the torsional bifurcation buckling of functionally graded (FG) multilayer graphene platelet reinforced composite (GPLRC) cylindrical shells are obtained. Five types of graphene platelets (GPLs) distributions are considered, and a slope factor is introduced to adjust the distribution profile of the GPLs. Within the framework of Donnell’s shell theory and with the aid symplectic mathematics, a set of lower-order Hamiltonian canonical equations are established and solved analytically. Consequently, the critical buckling loads and corresponding buckling mode shapes of the GPLRC shells are obtained. The effects of various factors, including the geometric parameters, boundary conditions and material properties on the torsional buckling behaviors are investigated and discussed in detail.

Strength determination for band-loaded thin cylinders

Cylindrical shells are often subjected to local inward loads normal to the shell that arise over restricted zones. A simple axisymmetric example is that of the ring-loaded cylinder, in which an inward line load around the circumference causes either plasticity or buckling. The ring-loaded cylinder problem is highly relevant to shell junctions in silos, tanks and similar assemblies of shell segments. The band load is similar to the ring load in which a band of inward axisymmetric pressure is applied over a finite height. When the height is very small, the situation approaches the ring-loaded case, and when the height is very large, it approaches the uniformly pressurised case. This article first thoroughly explores the two limiting cases of plastic collapse and linear bifurcation buckling, which must both be fully defined before a complete description of the nonlinear and imperfection-sensitive strengths of such shells can be described within the framework of the European standard for shells (EN 1993-1-6). Finally, the application of the reference resistance design (RRD) over the complete range of geometries for the perfect structure is shown using the outcome of the limiting cases.

Buckling of Corroded Torispherical Shells Under External Pressure

The current paper examines the effects of corrosion induced wall thinning on buckling of domed closures onto cylindrical vessels. It is assumed that corrosion is axisymmetric and that the wall is corroded on inside, only. The ratio of corroded wall thickness, tc, to the non-corroded thickness, t, is varied between 0.10 ≤ tc/t ≤ 1.0. Both depth of corrosion and its meridional extend are varied during numerical calculations. Three modelling scenarios for placement of corrosion are considered: (i) corrosion confined to the knuckle, (ii) corrosion spanning evenly the knuckle and spherical parts, and (iii) patchtype area positioned at the apex. Numerical results indicate that the following factors influence buckling performance of the dome: (i) meridional position of corroded area, (ii) depth of corrosion itself, and (iii) meridional span of corroded wall. For example, wall thinning of 10 % over 10 % of meridional length causes almost 20 % drop in buckling strength. The largest drop of load carrying capacity is found when the corroded wall is at the knuckle/crown junction. Here it is shown that assessment of strength based on the collapse mechanism is not only wrong but dangerous. For the case of the corroded dome, the collapse pressure overestimates the load carrying capacity associated with asymmetric bifurcation buckling by 40 %.

Linearized theory, the second variation and bifurcation of equilibria

This chapter develops the criterion of the second variation of energy and its connection to bifurcation buckling. It includes a non-standard treatment accounting for local constraints.

Nonlinear Stability Analysis of Elastic Cylinders under Global Bending

The cylindrical shells under global bending with different geometric parameters display different failure behavior. The size of typical buckles under axial compressive stress regimes is rather small and extends over a very small zone, with the axial compressive stress reaching the critical value. The first estimate of the elastic buckling strength in bending is the condition in which the most compressed fiber reaches the buckling stress for uniform axial compression. For short cylinders, local bifurcation buckling occurs at the middle of the most compressed side of the shell, and geometric nonlinearity has a little effect on the buckling strength, while for medium-length and long cylinders, the geometric nonlinearity and the ovalization of the cross-section should be considered. This paper explores the failure behavior in elastic cylinders in pure bending.