caa a22 4500 463244265 CHVBK 20180405153321.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00158-005-0602-5 doi (NATIONALLICENCE)springer-10.1007/s00158-005-0602-5 Michell cantilevers constructed within trapezoidal domains [Elektronische Daten] Part IV: Complete exact solutions of selected optimal designs and their approximations by trusses of finite number of joints [C. Graczykowski, T. Lewiński] The paper concerns the Michell-like cantilevers transmitting a point load to a straight segment of a support. The feasible domain is of trapezoidal infinite shape, as in the previous parts of the paper. The ratio of allowable stresses in tension and compression is arbitrary, not necessarily equal to 1. The present, last part of the paper includes detailed geometric and static analyses of the optimal cantilevers for various admissible data, thus providing new benchmarks of topology optimization. All results are found by using analytical methods developed in the previous parts of the paper. Particular attention is put on the force field distribution within the fibrous domains. These force fields turn out to be defined in certain subdomains forming a static division. The volumes of the optimal cantilevers are computed in two manners: by direct integration of the density of fibres and summing it up with the volume of the reinforcing bars of finite cross sections, and by using the kinematic formula of Michell according to which the volume is proportional to the virtual work. The examples analysed prove that both approaches lead to identical results of the volumes, thus showing that the possible duality gaps vanish. The analytical solutions are verified by considering appropriately chosen sequences of trusses of finite number of joints converging to the exact Michell cantilevers. Springer-Verlag, 2006 Graczykowski C. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049, Warsaw, Poland aut Lewiński T. Institute of Structural Mechanics, Faculty of Civil Engineering, Warsaw University of Technology, al.Armii Ludowej 16, 00-637, Warsaw, Poland aut Structural and Multidisciplinary Optimization Springer-Verlag 33/2(2007-02-01), 113-129 1615-147X 33:2<113 2007 33 158 https://doi.org/10.1007/s00158-005-0602-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00158-005-0602-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Graczykowski C. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049, Warsaw, Poland aut NATIONALLICENCE 700 1- Lewiński T. Institute of Structural Mechanics, Faculty of Civil Engineering, Warsaw University of Technology, al.Armii Ludowej 16, 00-637, Warsaw, Poland aut NATIONALLICENCE 773 0- Structural and Multidisciplinary Optimization Springer-Verlag 33/2(2007-02-01), 113-129 1615-147X 33:2<113 2007 33 158 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer