Implementation Of Asymptotic Homogenization Method Research Articles

Corrigendum to “Study on equivalent mechanical properties of U-shaped bellows based on novel implementation of asymptotic homogenization method” [Reg Stud Mar. Struct. 103622, March 2024]

Corrigendum to “Study on equivalent mechanical properties of U-shaped bellows based on novel implementation of asymptotic homogenization method” [Reg Stud Mar. Struct. 103622, March 2024]

Study on equivalent mechanical properties of U-shaped bellows based on novel implementation of asymptotic homogenization method

As typical metal thin-walled structure, bellows are used widely in various engineering fields, especially in storage and transportation of floating liquefied natural gas (FLNG) system on the sea. While the shapes of the bellows are relatively complex with the characteristics of geometric nonlinearity in the structure, it is quite challenging to calculate basic mechanical properties of the bellows accurately through theoretical analysis. Concurrently, both numerical simulation and experiments also require high computational and economic cost. Given the typical one-dimensional periodicity of the structure of U-shaped bellows, novel implementation of asymptotic homogenization (NIAH) method was secondary developed in finite element software and unit-cell model of the whole structure with periodic boundary conditions was established, realizing equivalent analysis of the overall mechanical properties of the bellows accurately and efficiently. By comparing the NIAH equivalent results with the fine finite element model results, it was found that the relative error was within 3.00 % and the calculation cost was reduced by 40 times. Compared with the experimental results, the error of NIAH equivalent results was also less than 6.00 %, which verified the accuracy and high efficiency of the NIAH equivalent method. Furthermore, the influence of unit-cell model with different structural sizes on the prediction accuracy of the NIAH equivalent stiffness results of the bellows was also discussed. This study provides a new effective method for the design and analysis of the structure of bellows.

Equivalent mechanical property calculation method of mini-channels in printed circuit heat exchanger

Printed circuit heat exchanger (PCHE) is a critical component to transfer heat from the primary loop to the secondary loop in supercritical carbon dioxide (SCO2) Brayton cycle system used for Generation IV nuclear reactors. The PCHE is operated at high temperature and high pressure, and thus the thermo-mechanical analysis is essential to its structural safety. However, it is difficult to directly model the whole PCHE by the finite element method because the PCHE is composed of large amounts of mini-channels. The simplified approach based on equivalent-homogeneous-solid concept was used by many researchers, but accurate method to calculate the equivalent mechanical properties of PCHE mini-channels is lacking. In this paper, an asymptotic homogenization method is proposed to calculate the equivalent mechanical properties of PCHE mini-channels. Firstly, the periodicity of mini-channels is considered as a small parameter, and the statement of equivalent elasticity matrix of mini-channels is derived in the form of stain energy of the unit cells. Secondly, numerical implementation of asymptotic homogenization method for a unit cell in the PCHE mini-channels is conducted. The equivalent Young’s modulus, Poisson’s ratio and shear modulus of mini-channels are fitted as functions of temperature. Finally, the thermo-mechanical performance of the equivalent PCHE core model is compared with the actual model. The results show that the maximum deviations in mechanical and thermal deformations between the equivalent and actual PCHE core models are less than 2.4% and 1% respectively. However, the computation time of the equivalent model is a factor of 45–190 below the value of actual model.

The effect of micromechanics models on mechanical property predictions for short fiber composites

The Tandon-Weng (T-W), the Halpin-Tsai (H-T) micromechanical models and a novel numerical implementation of asymptotic homogenization method (NIAH) for determining the stiffness of unidirectional orientation short fiber composites are compared. Based on rigorous mathematical theory, NIAH can be easily implemented using commercial software as a black box as representative volume approaches. Representative volume element (RVE) models were generated using random sequential adsorption technique (RSA) based on the optimal Latin hypercube sampling method. For arbitrary fiber orientation, the NIAH approach was compared with orientation averaging with the T-W and the H-T micromechanical models. Agreement between the three approaches in predicting the effective properties of short fiber composites was found to be excellent. Finally, the results calculated with the three approaches were compared with experimental values. It is shown that the three approaches in this paper are in quite good agreement with measured values. However, for random oriented short fiber composites with fiber length and fiber diameter distribution, the NIAH method still can provide calculated results with sufficient prediction accuracy, and the other two methods are not any more effective.

Buckling surrogate-based optimization framework for hierarchical stiffened composite shells by enhanced variance reduction method

The surrogate-based optimization of hierarchical stiffened composite shells against buckling is a typical multimodal and multivariables optimization problem. To improve the computational efficiency and global optimizing ability of the surrogate-based optimization of hierarchical stiffened composite shells, an enhanced variance reduction method based on Latinized partially stratified sampling and multifidelity analysis methods is proposed in this paper and then integrated into the surrogate-based optimization framework. In the offline step of the optimization framework, candidate pairing strategies of design variables are generated by Latinized partially stratified sampling and compared by performing priori optimizations based on the low-fidelity analysis method, and the optimal pairing strategy is therefore determined. On the basis of the optimal pairing strategy, the surrogate-based optimization is carried out using the high-fidelity analysis method in the online step. With less computational cost in the offline step, the proposed enhanced variance reduction method overcomes the limitation of Latinized partially stratified sampling that the optimal pairing strategy is not obvious in complex problems. Then, extensive optimization examples are carried out to verify the efficiency and effectiveness of the proposed optimization framework. Given an approximate computational cost, the optimal buckling result of the proposed framework using enhanced variance reduction method increases by 18.2% than that of the traditional framework based on Latin hypercube sampling. In particular, the advantage of enhanced variance reduction method in the space-filling ability is highlighted in comparison to Latin hypercube sampling. When achieving an approximate global optimal solution, the proposed framework reduces the total computational cost by 76.3% than the traditional framework. Finally, the numerical implementation of asymptotic homogenization method is used herein for the accurate prediction of effective stiffness coefficients of the initial design and optimal results. Through comparison, it is concluded that the high axial stiffness and bending stiffness are the main mechanism for the high load-carrying capacity of optimal results.

Fast procedure for Non-uniform optimum design of stiffened shells under buckling constraint

For tailoring the non-uniform axial compression, each sub-panel of stiffened shells should be designed separately to achieve a high load-carrying efficiency. Motivated by the challenge caused by numerous variables and high computational cost, a fast procedure for the minimum weight design of non-uniform stiffened shells under buckling constraint is proposed, which decomposes a hyper multi-dimensional problem into a hierarchical optimization with two levels. To facilitate the post-buckling optimization, an efficient equivalent analysis model of stiffened shells is developed based on the Numerical Implementation of Asymptotic Homogenization Method. In particular, the effects of non-uniform load, internal pressure and geometric imperfections are taken into account during the optimization. Finally, a typical fuel tank of launch vehicle is utilized to demonstrate the effectiveness of the proposed procedure, and detailed comparison with other optimization methodologies is made.

Two-scale topology design optimization of stiffened or porous plate subject to out-of-plane buckling constraint

This paper studies maximum out-of-plane buckling load design of thin bending plates for a given amount of material. Two kinds of plates are considered. One is made of periodic homogeneous porous material. Another is uniformly stiffened solid plate. The plate material, thickness, design domain of its middle plane and boundary conditions are given. The pattern of prescribed in-plane external load or displacements along the part of boundaries, which move freely, is given. Both plate topology and micro-structural topology of porous material or stiffener layout are concurrently optimized. The artificial element material densities in both macro and micro-scale are chosen as design variables. The volume preserving nonlinear density filter is applied to obtain the black-white optimum topology and comparison of its different sensitivities is made to show the reason for oscillation during optimization process in Appendix. The new numerical implementation of asymptotic homogenization method (NIAH, Cheng (Acta Mech Sinica 29(4): 550---556, 2013) and Cai (Int J Solids Struct 51(1), 284---292, 2014) is applied to homogenization of periodic plate structures and analytic sensitivity analysis of effective stiffness with respect to the topological design variables in both macro-scale and micro-scale. On basis of that, this paper implements the sensitivity analysis of out-of-plane buckling load by using commercial FEA software and enables the application of gradient-based search algorithm in optimization. Several numerical implementation details are discussed. Three numerical examples are given to show the validity of this method.

Integrated optimization of hybrid-stiffness stiffened shells based on sub-panel elements

A concept of hybrid-stiffness stiffened shell is proposed based on sub-panel elements to achieve a simultaneous buckling pattern, which can provide enhanced design flexibility to fully explore the load-carrying capacity of structures. Then, a novel hybrid model is established to improve the computational efficiency of post-buckling analysis for stiffened shells, where the Numerical Implementation of Asymptotic Homogenization Method is utilized to smear out the stiffeners. On this basis, an integrated optimization framework of sub-panel configurations and weld lands for stiffened shells is presented. Illustrative examples with single and multiple cutouts demonstrate the effectiveness of the proposed framework based on the concept of hybrid-stiffness stiffened shell.

On predicting the effective elastic properties of polymer nanocomposites by novel numerical implementation of asymptotic homogenization method

The main issue of this paper is an attempt to predict the elastic properties of PVC/ABS/nano-CaCO3 polymer nanocomposites by coupling data of microstructure analysis and mechanical tests with a micro-mechanics analysis. The novel numerical implementation of asymptotic homogenization (NIAH) method is compared with the representative volume element (RVE) method under Dirichlet and Neumann boundary conditions. Numerical simulation results show that the NIAH method is more reasonable and accurate for simulating the micro-mechanical properties of periodic composite materials. In order to account for two kinds of particles spatial distribution in nanocomposites, statistical asymptotic homogenization (AH) method is performed by assigning randomness to the spatial distribution for the two kinds of particles in the unit cell. With increase of the number of the unit cell particles, the results of NIAH method converge to a stable value. We also show that in the case of fixed-size of the unit cell, the average mechanical properties of the obtained results converge to the stable value with the increase of the number of random configurations realization. In this paper, we use the unit cell containing the minimum number of particles for different weight ratio of two kinds of particles to obtain the effective mechanical properties by averaging simulation results of many samples of different configurations in the unit cell. Based on the results obtained, it can be concluded that spatial distribution for the two kinds of particles in the unit cell has a significant impact on the material macroscopic elastic properties. Furthermore, the method is more efficient to predict the mean values of the elastic properties than the experimental dispersions.

Hybrid analysis and optimization of hierarchical stiffened plates based on asymptotic homogenization method

As a potential aerospace structural concept, hierarchical stiffened plates under axial compression are characterized by multiple local features, which lead to the buckling analysis and optimization suffering from heavy computational costs, by means of exact Finite Element Method (FEM). Thus, an efficient and simple hybrid framework for the buckling analysis and optimization of hierarchical stiffened plates is presented in this study. Firstly, the skin and minor stiffeners are equivalent to an unstiffened anisotropic plate based on a novel numerical implementation of asymptotic homogenization method (NIAH), which can be easily realized using commercial software as a black box, indicating a strong applicability for rather complicated minor stiffener configurations. Then, the equivalent plate together with major stiffeners can be treated as a hybrid model to be calculated by FEM. Further, a surrogate-based optimization based on this hybrid model is performed. Finally, three illustrative examples are established to demonstrate the effectiveness and simplicity of the proposed framework.

Novel numerical implementation of asymptotic homogenization method for periodic plate structures

The present paper develops and implements finite element formulation for the asymptotic homogenization theory for periodic composite plate and shell structures, earlier developed in Kalamkarov (1987) and Kalamkarov (1992), and thus adopts this analytical method for the analysis of periodic inhomogeneous plates and shells with more complicated periodic microstructures. It provides a benchmark test platform for evaluating various methods such as representative volume approaches to calculate effective properties. Furthermore, the new numerical implementation (Cheng et al., 2013) of asymptotic homogenization method of 2D and 3D materials with periodic microstructure is shown to be directly applicable to predict effective properties of periodic plates without any complicated mathematical derivation. The new numerical implementation is based on the rigorous mathematical foundation of the asymptotic homogenization method, and also simplicity similar to the representative volume method. It can be applied easily using commercial software as a black box. Different kinds of elements and modeling techniques available in commercial software can be used to discretize the unit cell. Several numerical examples are given to demonstrate the validity of the proposed methods.