A nodal-based optimization method for the design of continuous fiber-reinforced structures

The mechanical performance of fiber-reinforced structures highly relies on fibers' paths in the matrix material. Unlike the level set method that offsets the zero-level contours of a higher-dimensional function, this work shifts the nodes of a truss network within an optimization framework to design individual paths specifically. All intersection manners of a single fiber with the rectangular continuum element are considered in the finite analysis to retrieve mechanical responses within an acceptable error margin numerically. The design variables, namely node coordinates, are updated via the method of moving asymptotes under the guide of the sensitivity of the objective function, which is smoothed using a radial basis function. After each optimization iteration, the paths are slightly adjusted to avoid twisting problems and control fiber gaps using a polynomial interpolation scheme. Numerical examples illustrate that the proposed method can generate elegant fiber paths within a few steps. In the meantime, the optimization efficiency is improved as the design variables are significantly reduced. Compared with existing methods, we found that lower objective values can be achieved as allowing nodes to move freely in the design domain guarantees a global minimum theoretically.