Engineering analysis of complex structures or mechanical systems typically involves contact with multiple components, large deformation, and material nonlinearity, which requires the application of nonlinear finite element methods. Despite the advancement of commercial software for finite element analysis (FEA), nonlinear FEA of a multi-component mechanical assembly will take hours to days, and even weeks to complete. It is highly desired to develop a reduced-order model for a family of complex structures that can reduce an original problems’ complexity and degree of freedom but has a reasonably small discrepancy with the full model and significantly reduces the computation time.

 

The typical approach to construct a reduced model includes 1) the response surface method via numerical design of experiments and, 2) the simplified physics approach. In this paper, it is proposed to develop a reduced model through the combination of simplified physics, dimensional analysis \[1\], and numerical design of experiments. First, a simplified physics model is created through simplification such that basic mechanics is kept, and ideally, an analytical solution can be used. The simplified model is then corrected through numerical design of experiment (DOE) for a refined simplified model. To make these simplifications generalizable, dimensional analysis is introduced in our process to group different parameters within the model. Fundamentally, dimensional analysis is a method to reduce the number and complexity of variables for engineering analysis. Up to four dimensions can be reduced, depending on the physical units \[mass (*M*), length (*L*), time (*T*), and temperature (*ϑ*)\] involved in the problem using groupings of variables in dimensionless forms. Dimensional analysis creates multiple benefits for analysis including compact variable forms, generality of relations, and discovering new scaling laws.

 

The approach is applied to the construction of a reduced order model for the analysis of a downhole plug \[2\]. The set of equations in the model includes elastic stress from uniformly distributed pressure on a thick wall cylinder, a stress concentration factor function for discontinuous pressure, and Neuber’s rule for plasticity correction. The reduced-order model is verified by full-scale FEA models and is validated through physical tests. The reduced-order model has been implemented in a spreadsheet and takes seconds to complete a design calculation, in contrast to hours using a full FEA model, enabling engineers’ quick evaluation of the corresponding designs.

 

REFERENCES

A. Zhong, Using FEA to create derivative designs with successful base designs, NAFEMS World Congress, June 17-20, 2019, Quebec City, Canada

B. Pickle and T. Swan, Slickline-Retrievable Wellhead Plugs and Downhole Plugging System Provides Wellbore Integration for Extreme HPHT Environments, OTC-23630,


Reduced Order Model for Efficient Engineering Analysis

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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