Aggressive submodelling of stress concentrations

For some "nite element analyses of stresses in engineering components, low-order elements can be preferred. This choice, however, results in slow convergence, especially at key stress concentrations. To overcome this di$culty, submodelling of stress concentrators can be employed. With submodelling, a subregion within the original global con"guration and centred on the stress concentrator of interest is analysed by itself, with a consequent reduction in computation. The more aggressive the submodelling, the smaller the subregion and the greater the computational savings. To realize such savings in actuality, it is necessary that appropriate boundary conditions be applied to the subregion. Some of these boundary conditions must be drawn from a global analysis of the original con"guration: then it is essential to ensure that such boundary conditions are determined su$ciently accurately. This paper describes a procedure for being reasonably certain that such is the case. The procedure is evaluated on a series of test problems and demonstrated on a contact application. Results show that good engineering estimates of peak stresses can be obtained even in regions of unusually high stress gradients. Furthermore, these estimates can be obtained in return for quite moderate levels of computational e!ort