An iterative procedure for finite-element stress analysis of frictional contact problems

Determining Individual Stresses Throughout a Pinned Aluminum Joint by Reflective Photoelasticity

“…While this would increase the number of coefficients to be evaluated, ample side conditions (currently 440 equations but could be increased by employing more experimental input data) are available. Knowing P, the prospects of evaluating ν c successfully are probably realistic since all of the physical boundary conditions of equation (9) would continue to be known and available, and ν c would appear as only an additional coefficient in equation (8) to be determined from the boundary conditions and measured photoelastic data (through τ 45 of equation (1)). Moreover, values of ν c do not vary greatly for stiff epoxy-like coatings.…”

“…Moreover, values of ν c do not vary greatly for stiff epoxy-like coatings. Knowing ν c but seeking P could be more challenging numerically as it implies not knowing R x of equations (5), (7), (8) and the last of equation (9). Since the photoelastic input information is associated with the particular value of the applied P, one could potentially also utilize some of equations (5) or (7) to aid in determining P (i.e., R x ) iteratively (initially assuming P at or near zero) by increasing the input/assumed value of P until its magnitude agrees with the integration of the vertically-projected components of σ rr and σ rθ from equation (5) on the contact area of the hole, or σ xx from equation (7) across the horizontal area at say x=0.…”

“…The Airy coefficients will consequently typically acquire new values at each load level-through the recorded photoelastic data, and equations (1), (8) and (9). This concept of considering a sequence of static conditions at incremental load levels is an advantage of the approach over purely analytical or numerical methods where the nonlinearity would have to be incorporated directly (e.g., through finding the size of the new contact surface between the pin and plate, perhaps by iteration, as the load is changed).…”

A general 3D contact smoothing method based on radial point interpolation

“…Accordingly, the tangential velocity υ T in (4) and (5) can be replaced by the tangential displacement increment u T . The details of solving (6) by way of the finite element method can be found in [25][26][27]. The main concern of this paper is contact surface smoothing that plays a significant role in accurate location of the projection point and continuity of the normal vector.…”

“…A number of reductions may be required due to the nonlinearity of contact problems. Once all the contacting points (without interpenetration or with interpenetration smaller than the allowed value g p ) are identified, an iterative procedure [25] is employed to solve the frictional contact problem of this time step, during which a constraint is applied to the normal displacement of each slave node in contact to impose the impenetrability condition [29]. A contacting slave node is forced to be on the contact surface and may slide on it, subject to the friction conditions.…”