Two of the selected real-life test structures were plane trusses. Evaluation of 3D-structures is also possible without modifications of the program. It was judged that the optimisation of a space truss would only provide a small degree of extra information about the developed method.
Different roof structures were optimised by the developed FE-optimisation modelling tool.
Optimisation models were built simultaneously with the FE-modelling. The operator activated various constraints. The designer must have sufficient experience to know generally the type of structure needed, i.e., where the K- and KT-joints should be located and that beams must be selected to connect the joints. The optimisation program itself, of course, determines the final location of the joint and the best beam profile. The selection of beams is important because other elements can join to the same node, for example with 3D-structures.
The roles of various load combinations on a structure are not within the scope of this thesis. It is assumed that the most severe load case has been defined before the optimisation of the structure.
The most dangerous load combination includes the partial safety factors of the load. The partial material and joint safety factors are included to the constraints of the optimisation model. Con-straint functions have some default values, which the user can modify before the optimisation.
Geometric constraints of the FE-geometry are important. This means that each time one node position changes, it may be needed to also update other node coordinates. This can be made using metric node coordinates, but this is time consuming and additionally there is a risk of the pro-gramming errors.
5.3.1 Multi-redundant boom
The optimisation of a multi-redundant boom structure was also performed as part of this research.
This was done in conjunction with the Laboratory of Virtual Engineering and Mechatronics who had responsibility for developing the new boom construction and its control system. The boom is a good representative of an optimised structure because booms of this type must be functional,
but also light and rigid. The boom was a new product concept and the construction was developed during the past four years.
The optimisation analysis made for the boom construction shows that the assumptions about the construction were generally correct. Other possible constructions were not optimal and therefore rejected.
The boom construction has a geometric constraint, which is difficult to take into account in the FE-optimisation modelling tool. The shape of the base plates was difficult to pre-program to the FE-program and a flexible math-component was needed. In this case, the boom structure was optimised by the intermediate phase program. The components were compiled and the shape of the boom was found without great difficulty. The coordinates of the nodes were parametric functions of the height, width and length of the boom.
5.3.2 Ridge roof B
The ridge roof case B was the most difficult optimisation problem. Each diagonal brace member was selected individually from the cross section table that contained 125 alternatives. Geometry of the K- and KT-joints were strictly constrained by the dimension ratios of the joining members.
The selection of the sufficient diagonals was time consuming. The FE-analysis was not performed if the one of the geometric constraints was violated, thus saving significant computer time.
6 CONCLUSIONS
The main goal of this research project was to investigate the possibilities for automating the modelling of truss type structures in an optimisation program. During this thesis project, three modelling and optimisation programs were developed and tested with practical mechanical engineering optimisation problems. The final program made use of the observed limitations from earlier program versions. The optimisation program combines a modern evolution based optimi-sation algorithm, an automated modelling tool that greatly reduces the effort between different model generations, and a finite element based analysis tool.
During the optimisation of real-life engineering structures, modelling was found to be the most time consuming phase in the optimisation. This naturally led to the development of an automated means for formulating the optimisation model. In total, three generations of modelling tools were developed, each generation included improvements based on experienced gained with previous generations. The first tool was flexible but was difficult to use when large optimisation models needed to be formulated. The third modelling tool was integrated in the FE-modelling program so that the user constructs a model suitable for optimisation during the process of constructing the preliminary FE-model. Constraints and objective functions are created automatically and require only minimal user input. A FE-model is constructed in a conventional manner. Elements and nodes contain objective and constraint functions. Constraint functions are deflection, tension, compression, bending, fatigue, hydraulic cylinder, buckling and strengths of the T-, K- and KT-joints. The designer activates the objectives, constraints and design variables during the FE modelling process. The members of the T-, K- and KT-joins have to be selected by the designer.
The user must also to select the interpolated slave nodes and master nodes so that multi-element beams remain straight. Coordinates of the nodes are continuous design variables and measures of the cross sections of the beam elements are discrete variables. The designer has to select tables where the discrete beam dimensions are selected during the optimisation. Default values of the constraints like safety factors can be changed by the user. The designer also has to select tables from which the beam dimensions and material properties are chosen during the optimisation. All selections are made with the aid of the graphical interface of the computer program. This automa-tion reduces significantly the modelling time and errors. Constraints are not editable in this version modern but limit state design concepts were used in the formulation of the constraint classes.
Three main objectives were considered when developing the automated modelling tool: flexibil-ity, speed and reliability. The final tool is a balanced compromise of objectives. Reliability and speed are high if the constraints are compiled, but flexibility is then low minimum. High flexibil-ity results in both poor reliabilflexibil-ity and low speed because a complex FE-model needs to be manu-ally linked to the optimisation model. This is a very time consuming process and mistakes are common.
The differential evolution algorithm used in this program can be used nearly as a black box. In practice, the user has to select only the population size. This value can be selected after only a few tests. The third modelling tool was tested with truss structures, which include from 200 to 300 constraints. Penalty functions are not needed in the final variation of the differential evolution algorithm used here.
The optimisation algorithm is tested using common test functions used for the evolution algo-rithms and was found to perform very well with only minor differences between the values obtained here and published ideal values.
The optimisation system, including optimisation algorithm, automated modelling routine and FE analysis programs, was then tested on several large steel structures optimisation problems. These structures were a hydraulically driven multi-redundant boom, a flat roof truss structure, and a ridge roof KT-structure. The progressive boom construction was selected as an optimisation case, because it was completely new concept and the structure of the best construction was uncertain.
The optimisation of the steel structure of the boom showed that the preliminary supposition was right. Two steel structures were selected for test cases for third generation modelling and optimi-sation program, because these includes quite few elements but numerous geometric constraints, which make almost all solutions infeasible. This is a demanding challenge for the optimisation algorithm. The FE-model, which has constructed from 14-degree of freedom elements, is a challenge for modelling tool. Especially with case B of the ridge roof truss, the optimisation model was easy to form. This problem was very complex in terms of element possibilities and constraints and more computer time would be required to achieve a fully optimal solution.