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We propose a new method for laminate stacking sequence optimization based on a two-level approximation and genetic algorithm (GA), and establish an optimization model including continuous size variables (thicknesses of plies) and discrete variables (0/1 variables that represent the existence of each ply). To solve this problem, a first-level approximate problem is constructed using the branched multipoint approximate (BMA) function. Since mixed-variables are involved in the first-level approximate problem, a new optimization strategy is introduced. The discrete variables are optimized through the GA. When calculating the fitness of each member in the population of GA, a second-level approximate problem that can be solved by the dual method is established to obtain the optimal thicknesses corresponding to the each given ply orientation sequence. The two-level approximation genetic algorithm optimization is performed starting from a ground laminate structure, which could include relatively arbitrarily discrete set of angles. The method is first applied to cylindrical laminate design examples to demonstrate its efficiency and accuracy compared with known methods. The capacity of the optimization strategy to solve more complex problems is then demonstrated using a design example. With the presented method, the stacking sequence in analytical tools can be directly taken as design variables and no intermediate variables need be adopted.

In this article, multiwalled carbon nanotube/natural rubber composites with resistance-strain sensitivity were prepared by solution method, when the electrical percolation threshold of multiwalled carbon nanotube is only ∼3.5 wt%. The mechanical properties and resistance-strain response sensitivity were studied and analyzed systematically. The dispersion of multiwalled carbon nanotubes in the natural rubber matrix was characterized by field-emission scanning electron microscope and X-ray diffractometer. The composite exhibits good deformation sensitivity (gauge factor >27), large strain sensing range (>200%), and high signal stability when multiwalled carbon nanotube content was appropriate. The composite is suited to application in strain monitoring of large deformation structures since the resistance-strain response is more stable when strain exceeds 100%. To understand the mechanism of the resistance-strain response, the ‘shoulder peak’ of resistance-strain curve was researched and explained by the digital image correlation method, and an analytical model was developed when considering the effects of electronic tunneling and hopping in multiwalled carbon nanotube networks. Both experiment and analytical results confirm the break-restructure process of multiwalled carbon nanotube networks under applied strain cause the resistance-strain response. Finally, the practical application of the composite to monitoring strain load of rubber isolation bearing was realized.

The dispersion, electrical conductivities, mechanical properties and resistance–strain response behaviors of multiwalled carbon nanotube (MWCNT)/natural rubber (NR) composites synthesized by the different processing conditions are systematically investigated at both macro- and micro-perspectives. Compared with the solution and flocculation methods, the two roll method produced the best MWCNTs distribution since the materials are mixed by strong shear stress between the two rolls. An excellent segregated conductive network is formed and that a low percolation threshold is obtained (~1 wt.%) by the two roll method. Different from the higher increases in conductivity for the composites obtained by the solution and flocculation methods when the MWCNT content is higher than 3 wt.%, the composite prepared by the two roll method displays obvious improvements in its mechanical properties. In addition, the two roll method promotes good stability, repeatability, and durability along with an ultrahigh sensitivity (GFmax = 974.2) and a large strain range (ε = 109%). The ‘shoulder peak’ phenomenon has not been observed in the composite prepared by the two roll method, confirming its potential for application as a large deformation monitoring sensor. Moreover, a mathematical model is proposed to explain the resistance–strain sensing mechanism.

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