In plane: This configuration may appear in checkerboard patterns, diagonal element chains or as isolated hinges. Corner contacts in nominally optimal topologies are caused by discretization errors associated with simple (e.g. four-node) elements, which grossly overestimate the stiffness of corner regions with stress concentrations. In fact, it was shown by Gaspar [1] that both checkerboard patterns and diagonal element chains may give an infinite compliance, if the latter is calculated by an exact analytical method. This makes them the worst possible solution, if an exact analysis is used in compliance minimization. Corner contacts may be suppressed by

1. A more accurate FE analysis of the ground elements.
2. Modification of the original problem by using geometrical constraints or "diffused" sensitivities (filters).
3. Employing a constraint preventing corner contacts directly.
4. Correcting selectively the discretization errors by appropriately penalizing corner contacts.

The approach 4. seems to be the most rational, because it rectifies the discretization errors, which lower incorrectly the value of the objective function (e.g. compliance). The proposed method is particularly effective in combination with the SIMP method, since the latter is a penalization method in its original form, and requires only a minor modification for corner contact control (CO-SIMP). An early corner contact function was suggested by Bendsoe [2]. Defining and employing new CCF's, continuous functions which have a high value for corner contacts and a low value for any other configuration around a node, as an objective a new mathematical programming process CO-SIMP was developed [3,4]. The CO-SIMP method in case of Michell's cantilever generates a similar result as the exact solution of that. The development of the CCF's properties, the concerning numerical method, the modified SIMP algorithm and extensive numerical examples will be reported at the meeting.

In space: The problem is more complex: a diagonal chain can be generated by corner connected elements in 3D or by edge connected elements in planes. The 3D checkerboard form is generated by four edge connected cubic elements. The eight elements around a node produce 256 possible black and white, solid or empty element configurations. The designed function is able to separate and penalize the possible corner contact and edge connections and give no penalization for the non- checkerboard compositions.

1

Rozvany, G.I.N., Querin, O.M., Gaspar, Z., Pomezanski, V., "Weight increasing effect of topology simplification", Struct. Multidisc. Optim. 25, 459-465, 2003. doi:10.1007/s00158-003-0334-3

2

Bendsoe, M.P., Diaz, A., Kikuchi, N., "Topology and generalized layout optimization of elastic structures", In Bendsoe, M.P., Mota Soares C.A., (editors), Topology design of structures, Proc NATO ARW, Sesimbra 1992, Kluwer, Dordrecht, 1993.

3

Pomezanski V., Querin O.M., Rozvany G.I.N., "CO-SIMP: extended SIMP algorithm with direct COrner COntact COntrol", Structural and Multidisciplinary Optimization, Springer, Volume 30, Number 2, 2004.

4

V. Pomezanski, "Numerical Methods to Avoid Topological Singularities", in Proceedings of the Eighth International Conference on Computational Structures Technology, B.H.V. Topping, G. Montero and R. Montenegro, (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 211, 2006. doi:10.4203/ccp.83.211

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