A Hybrid Design Optimization Method using Enriched Craig-Bampton Approach

A hybrid design optimization method is presented which combines a number of techniques such as Component Mode Synthesis (CMS), Design of Computer Experiments and Neural Networks for surrogate modeling with Genetic Algorithms and Sequential Quadratic Programming for optimization. In the method, the FE analysis is decomposed and reduced by a well-known CMS technique called the Craig-Bampton method. Since the optimization method requires CMS calculations of the updated model at each of its iterations due to the changes in the design variables, one can either reuse the reduction basis of the initial components or compute new reduction basis for the condensation of the system matrices. The first option usually leads to inaccurate results and the last one increases the omputation time. In the method, instead of using one of these options, the Enriched Craig-Bampton method, proposed by Masson et al., is employed for efficient optimization. New basis for the modified components are generated by extending the corresponding initial reduction basis with a set of static residual vectors which are calculated using prior knowledge of the initial component designs. Thus, time consuming complete component analyzes are prevented. A theoretical test problem is used for the demonstration of the method

An optimization method for dynamics of structures with repetitive component patterns

The occurrence of dynamic problems during the operation of machinery may have devastating effects on a product. Therefore, design optimization of these products becomes essential in order to meet safety criteria. In this research, a hybrid design optimization method is proposed where attention is focused on structures having repeating patterns in their geometries. In the proposed method, the analysis is decomposed but the optimization problem itself is treated as a whole. The model of an entire structure is obtained without modeling all the repetitive components using the merits of the Component Mode Synthesis method. Backpropagation Neural Networks are used for surrogate modeling. The optimization is performed using two techniques: Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP). GAs are utilized to increase the chance of finding the location of the global optimum and since this optimum may not be exact, SQP is employed afterwards to improve the solution. A theoretical test problem is used to demonstrate the method

Design Optimization Utilizing Dynamic Substructuring and Artificial Intelligence Techniques

In mechanical and structural systems, resonance may cause large strains and stresses which can lead to the failure of the system. Since it is often not possible to change the frequency content of the external load excitation, the phenomenon can only be avoided by updating the design of the structure. In this paper, a design optimization strategy based on the integration of the Component Mode Synthesis (CMS) method with numerical optimization techniques is presented. For reasons of numerical efficiency, a Finite Element (FE) model is represented by a surrogate model which is a function of the design parameters. The surrogate model is obtained in four steps: First, the reduced FE models of the components are derived using the CMS method. Then the components are aassembled to obtain the entire structural response. Afterwards the dynamic behavior is determined for a number of design parameter settings. Finally, the surrogate model representing the dynamic behavior is obtained. In this research, the surrogate model is determined using the Backpropagation Neural Networks which is then optimized using the Genetic Algorithms and Sequential Quadratic Programming method. The application of the introduced techniques is demonstrated on a simple test problem

Exact mean field inference in asymmetric kinetic Ising systems

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.Comment: 10 pages, 7 figure

The tail of the contact force distribution in static granular materials

We numerically study the distribution P(f) of contact forces in frictionless bead packs, by averaging over the ensemble of all possible force network configurations. We resort to umbrella sampling to resolve the asymptotic decay of P(f) for large f, and determine P(f) down to values of order 10^{-45} for ordered and disordered systems in two and three dimensions. Our findings unambiguously show that, in the ensemble approach, the force distributions decay much faster than exponentially: P(f) ~ exp(-f^{\alpha}), with alpha \approx 2.0 for 2D systems, and alpha \approx 1.7 for 3D systems.Comment: 4 pages, 4 figures, submitted to Phys. Rev.

An Investigation of Complex Mode Shapes

This paper presents an investigation of complex mode shape analysis caused by non-linear damping. Nowadays, most academics are accustomed to complex mode shapes, which are a characteristic of most axisymmetric structures. The topic was deeply investigated during the 1980s, sparking the sharpest debates about their physical existence or not. However, after nearly three decades, one question still stands, do we know all about complex mode shapes? This paper takes the dust off this topic again and explores how complex eigenvectors arise when the percentage frequency separation between two mode shapes is the same order of magnitude as the percentage damping. The difference between the past and present investigations relates to the non-linear damping that might arise from joint dynamics under various vibration amplitudes. Hence, the new research question is about the investigation of amplitude-dependent damping on the modal complexity. Why bother? There are several engineering applications in both space and aerospace where axisymmetric structures and joint dynamics can impair the numerical analysis that is currently performed. This paper does not offer any solutions but does expand the research on an unsolved challenge by identifying the questions posed.</p

Ensemble Theory for Force Networks in Hyperstatic Granular Matter

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution $P(f)$. For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a non-invertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting $P(f)$'s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a new perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.Comment: 17 pages, 17 figure