Dynamic substructuring and reanalysis methods in a surrogate based design optimization environment

Abstract In light weight structure design, vibration control is necessary to meet strict stability requirements and to improve the fatigue life of structural components. Due to ever-increasing demands on products, it is generally more convenient to include vibration prerequisites in a design process instead of using vibration control devices on fixed designs. One of the main difficulties associated to design optimization of complex and/or large structures is the numerous computationally demanding Finite Element (FE) calculations. The objective of this research is to present a novel strategy for efficient and accurate optimization of vibration characteristics of structures. In the proposed strategy, a sub-structuring method is utilized. The FE model of the complete structure is partitioned, educed and then reassembled. This increases the computational efficiency of dynamic analyses. Moreover, this method is coupled with a novel reanalysis technique to speed up the repeated structural analyses. These methods are finally embedded in a surrogate-based design optimization procedure. An academic test problem is used for the validation of this novel approach. Keywords Dynamic substructuring · Reanalysis methods · Surrogate-based optimizatio

On the use of absolute interface coordinates in the floating frame of reference formulation for flexible multibody dynamics

In this work a new formulation for flexible multibody systems is presented based on the floating frame formulation. In this method, the absolute interface coordinates are used as degrees of freedom. To this end, a coordinate transformation is established from the absolute floating frame coordinates and the local interface coordinates to the absolute interface coordinates. This is done by assuming linear theory of elasticity for a body’s local elastic deformation and by using the Craig–Bampton interface modes as local shape functions. In order to put this new method into perspective, relevant relations between inertial frame, corotational frame and floating frame formulations are explained. As such, this work provides a clear overview of how these three well-known and apparently different flexible multibody methods are related. An advantage of the method presented in this work is that the resulting equations of motion are of the differential rather than the differential-algebraic type. At the same time, it is possible to use well-developed model order reduction techniques on the flexible bodies locally. Hence, the method can be employed to construct superelements from arbitrarily shaped three dimensional elastic bodies, which can be used in a flexible multibody dynamics simulation. The method is validated by simulating the static and dynamic behavior of a number of flexible systems

Efficient Computation of Large Deformation of Spatial Flexure-Based Mechanisms in Design Optimizations

Design optimizations of flexure-based mechanisms take a lot of computation time, in particular when large deformations are involved. In an optimization procedure, statically deformed configurations of many designs have to be obtained, while finding the statically deformed configuration itself requires tens to hundreds of load step iterations. The kinematically started deformation method (KSD-method) (Dwarshuis, K.S., Aarts, R.G.K.M., Ellenbroek, M.H.M., and Brouwer, D.M., 2020, "Kinematically Started Efficient Position Analysis of Deformed Compliant Mechanisms Utilizing Data of Standard Joints," Mech. Mach. Theory, 152, p. 103911) computes deformed configurations fast by starting the computation from an approximation. This approximation is obtained by allowing the mechanism only to move in the compliant motion-direction, based on kinematic equations, using data of the flexure joints in the mechanism. This is possible as flexure-based mechanisms are typically designed to be kinematically determined in the motion directions. In this paper, the KSD-method is extended such that it can also be applied without joint-data, such that it is not necessary to maintain a database with joint-data. This paper also shows that the method can be used for mechanisms containing joints that allow full spatial motion. Several variants of the KSD-method are presented and evaluated for accuracy and required computation time. One variant, which uses joint-data, is 21 times faster and shows errors in stress and stiffness below 1% compared to a conventional multibody analysis on the same model. Another variant, which does not use joint-data, reduces the computation time by a factor of 14, keeping errors below 1%. The KSD-method is shown to be helpful in design optimizations of complex flexure mechanisms for large range of motion

On the coupling of reanalysis techniques with a surrogate-based design optimization method

In this research, a Surrogate-Based Optimization (SBO) method is coupled with reanalysis techniques to improve the computational efficiency during optimization even further. The reanalysis techniques are used to speed up a reduction and a substructuring method, Craig-Bampton, which is utilized at the analysis step of the proposed SBO strategy. This strategy is suitable for solving problems where the modal and the harmonic responses of structures are required to be modified. An academic test problem is utilized for the demonstration