Stiffness-to-density ratios

Compare the flexural stiffness to weight ratios for the following three plastic beams, (a) a solid beam of depth 12 nun, (b) a beam of foamed material 12 mm thick and (c) a composite beam consisting of an 8 mm thick foamed core sandwiched between two solid skin layers 2 mm thick. The ratio of densities of the solid and foamed material is 1.5. (hint consider unit width and unit length of beam). 

Titanium metal is a light metal with near half the density of copper (4540 kg.rn" ), exhibits an excellent strength-to-density ratio allowing one to use thinner and lightweight anode plates without sacrificing the mechanical stiffness of the cathode, and has an excellent corrosion resistance to various corrosive environments. The only drawbacks of titanium are its high electrical resistivity (42 pQ.cm) and the high cost of the mill products (e.g., sheet, plate, rods), which can reach 46 US /kg in some cases. 

The bending stiffness of a homogeneous beam of material 1 is ,/. Thus, the effective bending stiffness of the sandwich beam has been reduced by the factor a, by replacing the core by material 2 with a lower modulus 2 but with a lower density P2. However, the stiffness-to-weight ratio has been increased as shown by Example 9.2. 

Blends of HDPE-l-low density polyethylene were immiscible even in the molten state [43], and formed separate crystal structures with generally poorer properties [27,41,42,46-48,50,53-55]. On the other hand, one study observed that they formed mixed crystals with intermediate melting point [185]. Some studies reported that practical properties were proportional to blend ratio [56-60] and a few even showed synergistic improvement of properties such as film drawdown and stiffness [56, 57,61,62]. 

An approximate method for the response variability calculation of dynamical systems with uncertain stiffness and damping ratio can be found in Papadimitriou et al. (1995). This approach is based on complex mode analysis where the variability of each mode is analyzed separately and can efficiently treat a variety of probability distributions assumed for the system parameters. A probability density evolution method (PDEM) has also been developed for the dynamic response analysis of linear stochastic structures (Li and Chen 2004). In this method, a probability density evolution equation (PDEE) is derived according to the principle of preservation of probability. With the state equation expression, the PDEE is further reduced to a one-dimensional partial differential equation from which the instantaneous probability density function (PDF) of the response and its evolution are obtained. Finally, variability response functions have been recently proposed as an alternative to direct MCS for the accurate and efficient computation of the dynamic response of linear structural systems with rmcertain Young modulus (Papadopoulos and Kokkinos 2012). 

As a result, ultra high modulus carbon fibers are preferred to others for their high stiffness/ density ratio for a low CTE compared with titanium or aluminum. Since composites are preferred to metal parts, bonding becomes the mandatory technology for fastening parts, because drilling and the bolt/nut/rivet principle require holes which affect the mechanical properties of the joint due to concentrations of loads around sectioned fibers. 

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