Young's modulus-density chart for engineering materials, including woods. The performance index E 1/2 /ρ gives the performance of a material for resisting bending deflections: every point on a single line E 1/2 /ρ has the same value of E 1/2 /ρ. As the line moves to the upper left, the value of E 1/2 /ρ increases [3]

Contexts in source publication

Context 1

... for a typical softwood, such as pine, with a relative density of 0,33; the value í µí°¸ µí°¸ * 1 2 ⁄ í µí¼Œ * ⁄ ~ 7 GPa 1/2 m 3 Mg -1 , the value that can be considered close to the best engineering materials [3]. For the purpose of comparison of different structural materials, including woods, chart represented in Figure 2 can be applied. Young's modulus-density chart for engineering materials, including woods. ...

Context 2

... conclusion should be considered during the design and optimization process by the reason that under certain circumstances it is advisable to select rather MCMS structure with three rings than structure with two rings. The next graph Figure 22 provides dependency of second moment of area on crosssection area of the MCMS structures. Such results provided for the structures with configurations HEX100, REC100 and TRI100, for range of ring numbers (3,2 and 1) and range of unit's thicknesses (or number of lamination layers, from 1 to 5). ...

Context 3

... one in the Appendix I, Figure 165 presents second moment of area for different grid types, number of lamination layers and rings. The second graph ( Figure 23) shows the influence of the density gradient on the performance of MCMS column-shaped elements. For comparison, it was decided to select a MCMS column with configuration HEX100 and uniform material redistribution. ...

Context 4

... MCMS module in combination with direct extrusion method is able to create manufacture-ready geometry provided in Figure 24. Such cellular structures, during the manufacture preparation stage, can be subdivided into separate tubes with responsible geometrical data and titled with unique ID like "#035-0014 / HEX100 / 5L-5". ...

Context 5

... course, for statistical and practical reasons it is possible as well to extract necessary information concerning the whole MCMS element such total length of 3 m, border thickness of 5 mm, cross-section area of 0,259 m 2 and consequent taking into account density of 2400 kg/m 3 total column's weight of 1864,8 kg, respectively with 0,777 m 3 of concrete. Additionally, for the purpose of production, MCMS module has functionality to generate textile reinforcement 3D geometry ( Figure 25) and calculate required number of reinforcement. Geometry module itself calculates just length of the textile reinforcement 2D curve that afterwards, by taking into account extrusion mechanism (direct extrusion or loft), can be applied for calculation of required area of the textile reinforcement. ...

Context 6

... more details, connection principles and respective elements will be provided within the scope of the next section No.4.3. The only thing that should be mentioned currently, is the fact that still the same MCMS geometry module able to generate connection elements in 3D (Figure 26), considering the design results of the cellular structure. One more time, connectors provided with ID formulated in the same way. ...

Context 7

... MCMS connection solution additionally was subdivided into two feasible approaches. Thus, first or, according to the accepted label, basic connection mode represented in Figure 27. It can be clearly seen from the figure that two initially separate MCMS units supposed to be connect by the so-called c-unit (connection-unit) that represent by itself typical so-called dowel connection. ...

Context 8

... next connection mode, in fact, represent itself application of the c-units (dowels) but with some extension. Besides the dowels, MCMS structures assumed to be connected additionally by the randomly ended cellular units ( Figure 28) to provide some extra surface for adhesive connection. In both connection modes, it is assumed to connect concrete part not only by friction but obviously by adding a special cement based adhesive agent ( [9] for reference) for gluing. ...

Context 9

... sections represent cellular geometry solutions to be applied for concrete structures and development of large scale objects, such as buildings, bridges, etc. Concerning applied geometry, United States Patent No: US 7,232,605 B2, [10] can be considered as project focused on the similar concepts of structural morphology ( Figure 29). The invention focused on natural-based composites or biocomposites that can serve as a sustainable alternative to synthetic load-bearing panels by designing them and manufacturing them in novel sandwich structures obtained from optimized hybrid designs that encompass material constituents, shape and scale effects [10]. ...

Context 10

... is known that each single tree starts with a thin, young stem and afterwards grow up by adding ring after ring. By such mechanism, tree is able to adapt own strength for the growing volume of a crown (see Figure 32), and as a result, growing wind actions. Exactly this mechanism seems interesting to be adapted within the MCMS concrete structures by two reasons. ...

Context 11

... this purpose, MCMS geometry module was equipped with fusion mode functionality. From Figure 17, it may be concluded that in order to initiate fusion mode execution it is required firstly to the start fusion toggle and secondly provide integer numbers to the special data field (Figure 42) of the MCMS tubes that should be removed. In consequence, MCMS structural element that was initial generated as a columnshaped element with HEX100 configuration and 2 rings, will be converted into the element with a cross-section represented in Figure 43. ...

Context 12

... one of the further possible improvements and application fields for the MCMS structures is combination of branching systems with a bridge functionality ( Figure 52). ...

Context 13

... it is correct to say that there is rather a set of Pareto optimal solutions or a Pareto Optimal Set (Pareto front) [14]. In order to illustrate Pareto front, further within the solution of nonlinear Figure 62 and Figure 63 provided. Obviously, each optimal point from the Pareto set can be used as a solution for the nonlinear multiobjective optimization problem. ...

Context 14

... only required aspect that should be mentioned is the fact that due to the stochastic nature of the genetic algorithms, Pareto set (front or line) will be generated not exactly but in approximation form. And such behaviour can be clearly seen in Figure 62 and Figure 63. ...

Context 15

... following Figure 80 shows a ratio calculated according to í µí°´í µí±€ 10 í µí±˜ í µí°´í µí±€ 10 10 ⁄ , where í µí°´í µí±€ 10 10 depicts the value of average mass for the generation No.10 and 10 previous generations. It may be concluded that in fact, both provided graphs ( Figure 81 and Figure 82) reflect similar results. Thus, recalling the beginning of the plateau behaviour depicted in Figure 75 by the number 3, it can be declared that the point when the program has to be terminated can be found on both graphs, by the selection of the appropriate decisive value; 0,1% for the first graph and 20 for the second graph. ...