How does the topology of a system affect its nonlinear dynamic response?

Here we demonstrated how changes in the geometry parameters of a V-shaped resonator can:

1. anticipate or posticipate the occurrence of Hopf bifurcations,

2. influence the saturation phenomena, and

3. lead to the co-existence of solutions.

Besides, we investigated the sensitivity of the dynamic response to small perturbations of the topology parameters. [Full text]

The L-shaped beam has long been regarded as the archetypal 2 degrees of freedom (DOFs) system that exhibits two-to-one internal resonance. Is this the only 2-DOF that has commensurate frequencies in a ratio 2-to-1? Is there any relationship between the number of commensurate harmonics and the number of members composing the system?

In this work we answered those questions unraveling:

1. the existence of a generalized manifold for the design of a two-member structure having commensurate frequencies (hereto dubbed V-shaped resonator),

2. the generalization of the manifold for structures with 3 commensurate harmonics, the Y- and Z-shaped resonator respectively, and

3. a rule of thumb for the design of resonators with N-commensurate harmonics. [Full text]

Classical methods adopted for topology optimization of continuum structures employ the material distribution concept, i.e. they assign a pseudo-density to each of the elements of a Finite Element model according to user-defined design criteria. Methods belonging to this class, such as SIMP (Solid Isotropic Material with Penalization) and BESO (Bi-directional Evolutional Structure Optimization), may exhibit computational issues like a) checkerboard patterns, b) mesh dependency, and c) singular topologies. One way to circumvent these computational issues is to couple the density-based approach to a filtering technique based on the sensitivity of the neighbor elements.

We developed a Graph-based Element Removal Method (GERM) used for the optimization of ground structures. The graph-based approach modifies the connectivity matrix of a Finite Element model based on the outcomes of a high-pass filtering scheme. Unlike other approaches, no pseudo densities are used. An avatar connectivity matrix is adopted to track all the changes made to the original system. Here we used the algorithm to synthesize compliant mechanisms and structures that exhibit commensurate frequencies. [Full text]

Although no undisputed definition exists for meta-heuristics exploration and exploitation those can be regarded as global and local search respectively. The tradeoff between exploration and exploitation has long been a relevant topic in evolutionary computation since it impacts the computational cost.

In this work, we introduced the breeding farm paradigm. We used the concept of linebreeding and outcrossing to enhance the global search of a Stud GA and, introduced an adaptive extinction to improve the local search and prevent the algorithm to get stuck in local optima. The algorithm is tested on benchmark optimization problems for the buckling load maximization of composite panels otherwise defined as constrained combinatorial problems. [Full text]