# Optimization Of Strut Diameters In Lattice Structures-Books Pdf

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processes Therefore a 3D CAD model can be build up for further design steps or data. processing for the following manufacturing of the optimized structure A respective NXOpen. program has been developed in the past to perform this task. Results for the Optimization of the Course of Lattice Structures. In 5 lattice structures which are adapted to the flux of force inside a respective part. are compared to a structure with a regular build up For that purpose a design space with. constraints and forces as depicted in Fig 2 is used as initial situation for the respective. optimizations,fixed bearing,shearing load, Fig 2 Design space constraints and load for optimization according to 5. The material used for the investigations is aluminium 6061 without thermal treatment. which has the following mechanical properties,Young s modulus 58 1 GPa. Limit of elasticity 55 MPa,Tensile strength 125 MPa. Density 2 711 g cm, The strut diameter for all structures is kept constant at 2 mm because only an adaption of. the course of the lattice structure should be considered. In the investigations the maximum von Mises comparison stress is determined in order. to rate the stability of the particular structures It is assumed that the maximum stress linearly. depends on the applied force on the structure Hence the force at the limit of elasticity can be. calculated The ratio of this load to the respective mass is used to compare the different. structures whereat a higher ratio indicates a better lightweight design. Initially a periodic structure build up is investigated This is the currently established. approach for the application of lattice structures in lightweight design The structure has a total. mass of 147 5 g The corresponding maximum value for the von Mises stress is 50 58 N mm. Under the assumption that this maximum stress linearly depends on the applied force a. maximum load of 406 6 N can be calculated for the obtaining of the limit of elasticity The ratio. of this force to the part s mass is 2 76 N g This value is used in order to compare the structure. with the other ones in the paper, Another structure which is presented in 5 is adapted to the flux of force in the design.
space see Fig 2 Here the single nodes of the structure are located along the fluxes of force in. main stress direction 1 2 and 3 These nodes are connected by straight struts to build up a. structure This build up has the advantage that almost no bending loads appear on the single. struts Analogue to the investigations presented before the diameters of the struts is set constant. The resulting structure and its constraints and loads can be seen in Fig 3 The mass of. this geometry is 83 58 g Thus the weight is 43 less than with conventional periodic. structures, Fig 3 Shear loaded beam with flux of force adapted lattice structure 5. The resulting maximum von Mises stress is 31 9 N mm Under the assumption that this. maximum stress linearly depends on the applied force a maximum load of 516 8 N can be. calculated for the obtaining of the limit of elasticity For the resulting ratio of this force to the. structure s mass a value of 6 18 N g can be calculated Hence the ratio has increased for 124. compared to the periodic structure, Thus it can be summarized that the adaption of the structure s course to the flux of force. in the design space has a great potential for lightweight design This is grounded in the fact that. almost no bending loads appear for this kind of structure 5. Uniform Optimization of Strut Diameters in Lattice Structures. The results of 5 which have been presented in the section before have been determined. for the arbitrary chosen diameter of 2 mm However to reach a predefined maximum von Mises. y 162 96x 2 003, stress or displacement additional investigations have to be done In the following section such. maximumcalculations,von Mises stress, are presented for a beam which is similar to the one presented before. For this purpose the structure is built up with 1D CBEAM elements and the strut. diameters are varied uniformly for the whole structure The influence of these strut diameters on. the mechanical properties in this case the maximum von Mises stress is determined The results. of these investigations can be seen in Fig 4,4545 maximum.
maximum von Mises stress,von Mises stress,maximum von Mises stress. strut diameter Stabdurchmesser mm, Fig 4 Maximum von Mises stress in dependence of the struts diameter. Because almost solely push and pull forces appear on the struts the maximum von Mises. stress is indirectly proportional to the cross sectional area and thereby indirectly proportional to. the squared diameter, For this and the following example the optimization goal is set to a maximum von Mises. stress of 32 N mm This result is used for strut diameters of 2 26 mm which means a mass of. 104 g for the structure In combination with the maximum von Mises stress of 31 8 N mm and. the force at the limit of elasticity of 518 4 N a ratio of force to mass of 4 97 N g can be. calculated This structure will also be the basis for the optimization of the single strut diameters. in the following section, Optimization of Strut Diameters in Lattice Structures. Beyond the optimizations of the course of lattice structures and the uniform optimization. of the struts diameter the cross section of the single struts can also be varied independently of. each other Thereby a constant material saturation can be reached within the part which leads to. an enhanced lightweight design The computer based proceeding for this optimization can be. seen in Fig 5,check if all struts meet,the predefined criteria.
Units N mm, Fig 12 Von Mises stress in a structure which was optimized with fixed nodes and constraints and an average. von Mises stress as optimization goal, Hence a proceeding for optimization of the struts diameters has been developed which. works without manual interaction for flux of force adapted structures. In structures which are not adapted to the flux of force however bending loads do appear. in the struts Therefore the last two proceedings do not work Here the first procedure has to be. adopted The optimization results for the investigated structures are summarized in Table 1. von Mises stress force at limit of maximum force,N mm elasticity N mass N g. 104 31 83 518 5 4 97,fixed nodes,106 31 38 525 8 4 96. maximum stress,released rotational,58 1 31 94 516 6 8 891.
DOFs maximum stress,fixed nodes,57 5 31 95 516 4 8 981. average stress, Table 1 Summary of the properties of the investigated structures. In Fig 13 a 3D simulation of the structure can be seen which has been optimized with. fixed nodes and constraints and an average von Mises stress as optimization goal Comparable to. Fig 12 with beam elements it is recognizable that the stresses in the struts are almost equal all. over the structure, Fig 13 Simulation of the optimized structure with 3D elements. However there do appear notch stresses in the nodes where the struts are connected. Therefore in future works there has to be found a better design for the nodes where the struts. merge smoother and therefore no notch stresses appear. Summary and Outlook, It has been exemplified that Additive Layer Manufacturing has a great potential for the. production of lightweight components Especially mesoscopic approaches like lattice structures. exhibit great properties for mass reduction However these structures are currently designed as. periodic patterns This leads to unfavorable bending loads in the single struts and uneven stresses. over the structure, To improve the structures build up an optimization approach has been introduced which.
adapts the course of the structure to the flux of force in a part The great potential of this. proceeding has been shown at the example of a shear loaded beam Here it was possible to. enhance the ratio of the maximum applicable force to the structures mass for 124 compared to. a periodic structure, Another optimization goal of the presented approach is the adaption of the struts. diameters with respect to the appearing stresses First an optimization has been introduced at. which the struts diameters are optimized uniformly until a predetermined maximum stress is. reached Thus it was possible to almost exactly reach the desired stress of 32 N mm However. the loads in the single struts were still varying, Therefore another second optimization approach has been applied Here the single struts. were adapted to their respective stresses individually However several different procedures. concerning the fixed and loose rotational degrees of freedom and the optimization goal. maximum of average von Mises stress had to be investigated to come to an optimization. procedure which does not lead to unwanted bending loads in the beams and which can be. performed without any manual interaction Thus the ratio of the maximum applicable force to. the structures mass could be enhanced for 80, However FEM calculations with a tree dimensional model of the structure have shown. that there are severe notch stresses appearing at the nodes where the beams are merging. Therefore a suitable node design will be developed in future works which realizes a smooth. connection of the struts and therefore reduces stress peaks. Beyond that another procedure for the optimization of the struts diameters will be. developed which makes it possible to reach a predefined stiffness of the structure with the. application of a minimum mass, Furthermore a rule based algorithm will be developed which is able to automatically. build up a structure that is adapted to the flux of force of a part Currently this step has to be. done with great manual effort, The presented approach for the optimization of lattice structures has been applied on the.
example of a shear loaded beam However further optimizations will be done on real. components from industry in the future Thereby the most benefit can be reached for parts which. are strongly accelerated or in industries where lightweight design is of essential importance. Therefore possible applications can be found in aviation and space flight in automotive. industries especially electric mobility and racing as well as in production and processing. Acknowledgements, We want to express our gratitude to the state government of Bavaria for its financial. support in the build up of the Fraunhofer Project Group for Resource Efficient Mechatronic. Processing Machines RMV Thereby the research work on the topic presented in this paper. was enabled,References, 1 Wohlers T 2010 Wohlers Reprt 2010 Additive Manufacturing State of the Industry. Wohlers Assiciates Inc Fort Collins 2010, 2 Zaeh M F Ott M 2011 Investigations on heat regulation of additive manufacturing. processes for metal structures CIRP Annals Manufacturing Technology 60 2011. 3 Kruth J P Levy G Klocke F Childs T H C 2007 Consolidation phenomena in. laser and powder based layered manufacturing Annals of the CIRP Vol 56 2 2007. 4 Reinhart G Teufelhart S Ott M Schilp J 2010 Potentials of Generative. Manufactured Components for Gaining Resource Efficiency of Production Facilities In. Neugebauer R Ed International Chemnitz Manufacturin Colloquium Reports form. the IWU Volume 54 703 710 Verlag Wissenschaftliche Scripten Auerbach 2010. 5 Teufelhart S 2012 Investigation of the Capability of Flux of Force Oriented Structures. for Lightweight Design Proceedings of the 2nd WGP Jahreskonferenz June 26th June. 27th 2012 Berlin Germany, 6 Reinhart G Teufelhart S 2011 Load Adapted Design of Generative Manufactured. Lattice Structures Physics Procedia 12 2011 pp 385 392. 7 Gibson L J Ashby M F 1997 Cellular Solids Structure Properties Second. Edition Cambridge University Press Cambridge 1997, 8 Rehme O 2010 Cellular Design for Laser Freeform Fabrication Cuvillier Verlag.
G ttingen 2010, 9 Reinhart G Teufelhart S 2011 Approach for Load adapted Optimization of. Generative Manufactured Lattice Structures In Spath D Ilg R Krause T Eds ICPR21. 21st International Conference on Production Research Conference Proceedings. 10 Reinhart G Teufelhart S Riss F 2012 Examination of the Geometry dependent. Anisotropic Material Behavior in Additive Layer Manufacturing for the Calculation of. Mesoscopic Lightweight Structures Proceedings of the Fraunhofer Direct Digital. Manufacturing Conference 2012 March 14th March 15th 2012 Berlin Germany. 11 Reinhart G Teufelhart S 2012 Optimization of Mechanical Loaded Lattice. Structures by Orientating their Struts Along the Flux of Force Proceedings of the 8th. CIRP Conference on Intelligent Computation in Manufacturing Engineering July 18th.

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