Date of Award
Doctor of Philosophy (PhD)
Professor M.A. Dokainish
The study presented in this thesis aims at fulfilling an industrial need for solution methods suitable for the analysis of complex nonlinear engineering problems. A finite element contact algorithm is developed, implemented and verified. Furthermore, the algorithm is used for the numerical simulation of the hydraulic expansion of tube joints.
A variational formulation of the general contact problem is presented where the virtual work principle is adopted to arrive at the discretized equilibrium equations for two generic bodies coming into contact under the effect of the applied loads. The discretized contact constraint equations are derived geometrically from the kinematics of the potential contact surface nodes. A direct engineering approach is used to develop a solution algorithm which is applicable for the analysis of contact problems in general. No assumptions are made regarding the geometry of the contacting bodies, the location and extent of contact and the nature of the external loading. A non-classical bi-Iinear friction model is introduced where micro tangential relative displacements are allowed even under very light normal traction. The bi-linear law may be reduced to the classical Coulomb's friction law as a special case. The algorithm is made capable of handling nonlinear continuum finite elements, i.e. elements with curved sides. The equilibrium equations are solved iteratively to calculate the contact nodal forces which remove any overlap without augmenting the contact constraint equations into the original system of equilibrium equations. Instead, the contact constraint equations are solved as an inner loop in the global nonlinear iteration loop which follows the full/modified Newton-Raphson iterative technique. The developed algorithm is implemented in the in-house general purpose non-linear finite element program INDAP¹ and verified through the solution of illustrative examples covering a wide range of contact problems of static, elastic, elasto-plastic, conformal and non-conformal contact interactions.
The developed contact algorithm is used along with two finite element models to simulate the hydraulic expansion of tube joints. A 2-D plane stress model is used to investigate the effects of the different material mechanical properties on the joint strength. A 2-D axisymmetric model is adopted to overcome the limited scope of the plane stress model. The feasibility of ignoring the geometric nonlinearity and the friction interaction are investigated. A 2³ complete factorial numerical experiment is adopted to study the main and interaction effects of the expansion pressure, the initial radial clearance and the coefficient of friction on the residual contact pressure, representing the joint integrity, and the maximum residual tensile stress along the tube inner and outer surfaces, representing the joint quality. A new explanation to the break-off the joint strength when the joint is further expanded beyond a well-defined optimum is suggested. The adequacy of some strength measures is explored. The effects of the initial stresses and the cold-work surface layer along the tube outer surface are investigated.
Ali, Usama Ahmed Abdelsalam, "A Finite Element Contact Algorithm Applied to the Analysis of Expanded Tube Joints" (1995). Open Access Dissertations and Theses. Paper 2275.