Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism

The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out.

Generalized Plane Strain Study of Rotational Autofrettage of Thick-Walled Cylinders—Part II: Numerical Evaluation

The theoretical modeling of the rotational autofrettage of a thick-walled cylinder based on the generalized plane strain assumption has been presented in part I of the paper. In order to access the potentiality of the proposed theoretical model, the numerical evaluation of the analytical solutions is important. This part of the paper presents numerical evaluation of the generalized plane strain model for typical thick-walled cylinders. The residual hoop stress generated in the rotational autofrettage of a typical gun barrel is compared with the residual hoop stresses in the conventional hydraulic and swage autofrettage processes. Comparison shows that the rotationally autofrettaged gun barrel is capable of producing the same level of compressive residual hoop stress at the inner surface as that of the hydraulic autofrettage. In order to corroborate the analytical solution, a three-dimensional finite element method (3D FEM) analysis of the rotational process is carried out in ANSYS finite element package and the results are compared with the theoretical results. The comparison shows a good matching of the results between the theoretical evaluation and the 3D FEM analysis. Finally, a short feasibility analysis of the rotational autofrettage process of typical cylinders is carried out for the practical realization of the process.

Generalized Plane Strain Study of Rotational Autofrettage of Thick-Walled Cylinders—Part I: Theoretical Analysis

In recent years, a few new methods of achieving autofrettage in thick-walled hollow cylinders have been developed. Rotational autofrettage is one of the new methods proposed recently for prestressing thick-walled cylinders. The principle of rotational autofrettage is based on inducing plastic deformation in the cylinder at the inner side and at its neighborhood by rotating the cylinder about its own axis at a certain angular velocity and subsequently bringing down it to zero angular velocity. However, the analysis of the process is still in its nascent stage. In order to establish the rotational autofrettage as a potential design procedure for prestressing thick-walled cylinders, accurate modeling of the process is necessary. In this paper, the rotational autofrettage for thick-walled cylinders is analyzed theoretically based on the generalized plane strain assumption. The closed form analytical solutions of the elasto-plastic stresses and strains and the residual stresses after unloading during the rotational autofrettage of a thick-walled cylinder are obtained. In Part II of the paper, the numerical evaluation of the theoretical model will be presented in order to assess its feasibility.

Thermo-Mechanical Response of Multilayered Cylinders Under Pressure and Thermal Loading With Generalized Plane Strain Condition

Multilayered cylindrical structures subject to pressure and thermal loading are commonly seen in many industries. In this study, the formulas for multilayered cylinders under pressure and thermal loading are derived with an assumption that the cylinders meet generalized plane strain condition, i.e., there is no external constraint in the axial direction and the axial growths of the cylindrical layers are the same. A numerical solution procedure for double-layered cylinders subject to both pressure and thermal load is developed and implemented in a mathcad program. To validate the solution, a finite element model for a double-layered cylinder is prepared with abaqus, and its responses under pressure and thermal loading are compared to those from the mathcad program. The algorithm of the method can be extended to three or more layered cylinders. The method developed in this study allows quick optimization and efficient design refinement for multilayered cylinders without running finite element analysis (FEA).

Three-dimensional thermo-mechanical analysis of continuous casting and comparison with two-dimensional models

In this study, a three-dimensional thermo-elasto-plastic model is developed for simulating a continuous casting process. The obtained results are compared with those from different two-dimensional analyses, which are based on plane stress, plane strain, and generalized plane strain assumptions. All analyses are carried out using the meshless local Petrov–Galerkin method. The effective heat capacity method is employed to simulate the phase change process. The von Mises yield criterion and elastic–perfectly-plastic model are used to simulate the stress state during the casting process; while, material parameters are assumed to be temperature-dependent. Based on the three-dimensional and two-dimensional models, numerical results are provided to determine the stress, displacement, and temperature fields induced in the cast material. It is observed that the present meshless local Petrov–Galerkin method is accurate in three-dimensional thermo-mechanical analysis of highly nonlinear phase change problems. Reasonable agreements are observed between the results obtained from the three-dimensional analysis with those retrieved by the generalized plane strain assumption. However, it is observed that the results obtained under plane stress/strain conditions have some significant differences with the results obtained from three-dimensional modeling of continuous casting.