Inversion of Functionally Graded Materials to Improve the Elastic Ultimate Bearing Capacity of Thick-Walled Hollow Cylinder

Abstract

Thick-walled hollow cylinder is an important class of engineering structure, the stress state of which depends on the loads and properties of the body materials. Under the assumptions of σθ-σr=c (σθ and σr denote the hoop stress and radial stress, respectively, c is a constant), inverse analysis of thick-walled hollow cylinder composed of functionally graded materials with uniform pressure acting on the outer surface is carried out. Analytical solutions for the Young’s modulus variation in the radial direction are obtained. It is found that only when the Young’s modulus E(r) is a specific monotone increasing function of the radius r, the pre-specified stress distribution can be satisfied. Comparing with classical homogeneous materials, stress concentration at the inner surface of hollow cylinder composed of functionally graded materials can be alleviated. Hence the elastic ultimate bearing capacity of hollow cylinder can be improved strikingly. For functionally graded materials, the elastic ultimate bearing capacity can be improved strikingly by increasing the thickness of cylinder, which is not so obvious for classical homogeneous materials.

The Elastic Solution of a Radial Heterogeneous Cylinder Subjected to Non-Uniform Distributed Normal and Tangential Loads

“…Horgan [13] performed a mechanical analysis of a functional gradient cylinder with an elastic modulus that radially varied as a power function under internal and external pressures and discussed the differences in the stress distributions between the actions of both the internal and external pressures. In addition, Lu [14] conducted an inversion analysis of a functionally graded material cylinder under the assumption that the stress state at every point on the cylinder was either = 1 or − = 2 and consequently developed an analytical solution for Young's modulus that varies with the radius.…”

Investigating Properties of Haydite Concrete by Using Taguchi Method

“…The application of FGM in the concrete engineerings can improve the force state of the structure, e.g., When the modulus of the inner-layer concrete is less than the outer one, the stress concentration on the cylinder inner surface will be relieved and the maximum tangential stress may be transferred from the inner surface of inner-layer to the inner surface of outer-layer [2]. While to the Functionally Graded Material (FGM), the elastic limit bearing capacity of the cylinder can be increased remarkably by using the continuous changing materials in the radial direction and through increasing its thickness [3].…”

Study on the Best Reinforcement Arrangement of Thick-Walled Cylinder

“…While to the Functionally Graded Material (FGM), the elastic limit bearing capacity of the cylinder can be increased remarkably by using the continuous changing materials in the radial direction and through increasing its thickness [2]. It can be known from [2] that, when the thick-walled cylinder is under a uniformly distributed pressure and Young's modulus of the material is continuous increasing in the radial direction, the stress distribution in the cylinder will be improved and the stress concentration can be avoided. [3] take a study of Optimum design method for double-layer thick-walled concrete cylinder with different Young's modulus on the basis of [2].…”

“…It can be known from [2] that, when the thick-walled cylinder is under a uniformly distributed pressure and Young's modulus of the material is continuous increasing in the radial direction, the stress distribution in the cylinder will be improved and the stress concentration can be avoided. [3] take a study of Optimum design method for double-layer thick-walled concrete cylinder with different Young's modulus on the basis of [2].…”

“…Steel Bars are not taken into account in [2]- [7] but in this paper. By changing the reinforcement arrangement in thick-walled cylinder to simulate the FGM, the stress distribution can be improved and the stress concentration can be avoided.…”