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Physically, initialization of crack surface is the initialization of new free surface in the solid body, forming a geometrical discontinuity. A numerical model that attempts to simulate cracks as discontinuity is classified as a “sharp crack model”. There are two approaches in “sharp crack” model: directly introduce crack as geometric discontinuity (see Figure 1), or … Read more
Genetic algorithm (GA) is a meta-heuristic technique for solving optimization problems. The algorithm mimics the behavior of nature, such as evolution and survival of the fittest. Basically, a population of n chromosomes are randomly created in the beginning. By applying operators, such as crossover and mutation, the population will be updated through many generations. Only … Read more
Roughly speaking, optimization is finding the feasible set of design variables that leads to optimum value of a specified objective (e.g. minimizing cost, minimizing weight, maximizing fracture toughness etc.). It is preferred that we can reach the global optimum, not a local one. This is also a challenge in solving optimization problem, because we do … Read more
The special characteristics of functionally graded materials (FGMs) is the continuous variation of material properties with respect to spatial coordinates. Bamboo, bone and human skin are examples of natural FGMs. In industry, FGMs can be manufactured as composite of at least two constituents, e.g. ceramics and metal. By special manufacturing process, the volume ratios of … Read more