A review of flexible multibody dynamics for gradient-based design optimization

Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

Design of stiffened panels for stress and buckling via topology optimization

This paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method.

Response optimization of underactuated vibration generators through dynamic structural modification and shaping of the excitation forces

Resonant vibration generators, such as vibratory feeders or ultrasonic sonotrodes, are often employed in manufacturing to generate harmonic vibrations with suitable amplitude, spatial shape, and frequency, in order to meet the process requirements. These underactuated systems are usually excited in open loop by few actuators, and therefore, it is not ensured that the desired response is correctly achieved, since the feasible motions should belong to the subset of the allowable motions. To achieve the closest approximation of the desired vibrations, some new solutions are here proposed. The first strategy is the optimal shaping of the harmonic forces exerted by the actuators, by solving an inverse dynamic problem through a coordinate transformation and the projection of the desired response onto the subspace of the allowable motion. By exploiting the formulation of such a subspace, a second approach that involves concurrently both the force shaping and the modification of the inertial and elastic system parameters is proposed. The idea of this approach is to exploit the modification of the elastic and inertial parameters to properly shape the allowable subspace in such a way that it spans the desired response. A solution method is developed, and analytical sensitivity analysis is proposed to choose the design variables. Validation is proposed through a linear vibratory feeder with a long flexible tray, taken from the literature. The results show the effectiveness of the proposed strategies that lead to a very precise approximation of the desired response.

Optimal In-Operation Redesign of Mechanical Systems Considering Vibrations—A New Methodology Based on Frequency-Band Constraint Formulation and Efficient Sensitivity Analysis

The vibrational behavior of components in mechanical systems like drives and robots can become critical under changes in the system properties or loading in operation. Such undesired vibration can lead to detrimental conditions including excess wear, fatigue, discomfort, and acoustic emissions. Systems are designed to avoid certain frequencies to avoid such problems, but system parameters can change during operation due damage, wear, or change in loading. An example is the change in system properties or operation state that then activates resonance frequencies in our system. Therefore, this work has the goal of modifying the modal behavior of a system to avoid vibrational problems. Methods of design optimization are applied to find a new optimum design for this altered condition. Here, this is limited to the addition of mass in order to move the resonance frequency out of critical ranges. This though requires a new formulation of the optimization problem. We propose a new constraint formulation to avoid frequency ranges. To increase efficiency, a reduced analytical sensitivity analysis is introduced. This methodology is demonstrated on two test cases: a two-mass oscillator followed by a test case of higher complexity which is a gear housing considering over 15,000 design variables. The results show that the optimization solution gives the position and amount of mass added, which is a discrete solution that is practically implementable.