Optimal shape design of elasto-static contacting bodies

An integrated approach to the shape optimization of elastic contact problems is presented. Research has been performed in several interdependent areas to accomplish this goal.A reliable finite element algorithm for numerical contact analysis of elastic bodies is used to solve the elastic contact problems. The adaptive incremental convex programming model to simulate the contact conditions between the two contacting bodies is used. The algorithm dealing with the contact problem in different contact conditions including advancing and receding contact types. The algorithm is currently limited to the solution of two dimensional plane stress, plane strain problems.The contact shape optimization problem is mathematically formulated.Various choices for the objective function to be minimized are discussed. Effective choices for the objective function are chosen, by minimizing the peak normal contact stress on the contact profile. However, the choice of the objective function depends on the nature of the particular problem and desired goal of the optimization process.Shape optimization is performed by direct modification of the contact surfaces through cubic spline curves. The use of the control nodes of the cubic spline curves as the optimization design variables instead of the coordinates of that points on the contacting surfaces give more advantages. These advantages are; reducing the dimensions of the optimization problem and consequently reduce the computational time, make the optimization problem more converge. The choice of the cubic spline to represent the optimal shape of the contacting surfaces gives surfaces, which meet the design and manufacturing requirements.The contact analysis algorithm was integrated with the augmented Lagrange multiplier algorithm to develop comprehensive shape design logic for the optimal shape design of contacting surfaces. The resulting model is applied to the solution of several design examples. It is found in each of these examples that substantial reduction in the normal contact stress can be realized by only slight modifications of the contacting profiles. The results can be utilized for specifying tolerances for the precision finishing of components.The optimal shape design of the contacting bodies is still considered as an extended area of research. The proposed model can be extended to consider the following points:1. The proposed model may be extended to include the three-dimensionalcontact problems.2. The proposed model may be extended to deal with contact problem withelastic plastic behavior.3. The proposed model may be extended to deal with contact problem with friction effects, which appears between the contacted surfaces in real cases.4. The proposed model may be extended to include the thermal effects on the material of contacted bodies, which appears in several engineering applications.5. The proposed model may be extended to include the contact problems with large deformation process such as metal forming and optimal shape die design.6. Instead of static loading, the proposed model may be extended to includethe effects of dynamic loads.7. Kinematics constraints, according to the objective of the designed mechanical component, should be inserted in the algorithm. This insures to have the required kinematics motion with optimal shape contact conditions.