Keywords: truss, optimization, connection, internal nodes, stability.

The ground structure of truss optimization usually represents the all to all except support to support node-connection theory [1]. This is to step over the internal node stability problem of including aligned compression bars in the result. This paper presents an algorithm to produce truss structures with a high number of nodes fitted to a square grid, where some of the outline nodes are supported or loaded and many outline and internal nodes are not:

• bars are across a maximum two cells of the grid,
• each bar starts at a node and terminates at an other one and
• along their length they do not connect a third node.

This type of structure generalization presents a topology optimization on a more complex connection network, more similar to the results of the plate structures found using the solid isotropic microstructure with penalties (SIMP) method [2,3,4,5].

The optimization process confirms the equilibrium and compatibility equations as equalities and lower and upper limits for all design variables as inequalities. The objective function is given in six different forms, as the sum of internal forces, the sum of the modification variables, work and some combination of them [6].

The proposed technique does not fulfil the internal bar stability (buckling), safety and economy requirements. The analysed structural forms are taken from the literature. The results produced are similar to the known solutions but these results contain a node-stability problem caused by a discretization error.

Concerning the results the ideal truss optimization in addition to the objective function also requires the following goals:

• Determine the minimal node and bar numbers for a static and solution.
• A minimum of two bars must be connected in each unsupported node.
• Each node has to be fixed both horizontally and vertically. Thus there is an 0°<alpha<180° angle between the two bars.

To confirm it in the optimization process an additional constraint or an extended objective function is necessary.

1

Pomezanski V., "Comparing the End-Results of the TNO and SIMP Methods of Topology Optimization", in Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing, Topping B.H.V., (Editor), Civil-Comp Press, Stirlingshire, United Kingdom, paper 35, 2007. doi:10.4203/ccp.86.35

2

Rozvany G.I.N., Querin O.M., Gáspár Z., Pomezanski V., "Extended optimality in topology design", Rozvany G., (ed), Struct. Multidisc. Optim., 24(3), 257-261, 2002. doi:10.1007/s00158-002-0235-x

3

Pomezanski V., Querin O.M., Rozvany G.I.N., "CO-SIMP: extended SIMP algorithm with direct COrner COntact COntrol", Struct. Multidisc. Optim., 30(2), 396-399, 2004. doi:10.1007/s00158-005-0514-4

4

Gaspar Z., Logo J., Rozvany G.I.N., "Addenda and Corrigenda...", Struct. Multidisc. Optim., 24, 338-342, 2002.

5

Pomezanski V., "Numerical Methods to Avoid Topological Singularities", in Proceedings of the Eighth International Conference on Computational Structures Technology, Topping B.H.V., Montero G., Montenegro R., (Editors), Civil-Comp Press, Stirlingshire, United Kingdom, paper 211, 2006. doi:10.4203/ccp.86.35

6

Pomezanski V., "Changing Connections Between Structural Elements During an Optimization Process", Journal of Computational and Applied Mechanics, 5(1), 117-127, 2004.

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