Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed…
Abstract
Based on the orthogonal approach for hybrid element methods, refined three‐dimensional isoparametric hybrid hexahedral elements have been developed. The behaviour of the proposed models are discussed in respect of coordinate invariance, spurious zero energy modes and the ability to pass the patch test. By adopting the orthogonality of strain energy, the element stiffness matrix can be decomposed into a series of stiffness matrices in which the implementational effectiveness can be improved. A number of examples is used to demonstrate the implementation efficiency, accuracy and distortion insensitivity of the proposed elements, and its capacity of handling nearly incompressible materials
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J.Y. Zhang and T.R. Hsu
A multi‐variable finite element algorithm based on the generalized Galerkin method is presented. This algorithm takes advantages from the hybrid finite element method and the…
Abstract
A multi‐variable finite element algorithm based on the generalized Galerkin method is presented. This algorithm takes advantages from the hybrid finite element method and the quasi‐conforming element method. Therefore, it has more flexibility and makes the hybrid and quasi‐conforming concepts easily applied to various physical problems. The formulation of a hybrid quadrilateral finite element with a unified singularity for both thermal and stress analyses has been derived using this algorithm. Some numerical examples are included to illustrate advantages of the hybrid algorithm in both stress and thermal analyses. It is also convenient to employ the algorithm in finite displacement problems.
Shi Zhang, Yun Zhang, Zhigao Huang, Huamin Zhou and Jianhui Li
– The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.
Abstract
Purpose
The purpose of this paper is to study the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary.
Design/methodology/approach
In this paper, three triangular flat shells developed by combining an excellent membrane element (OPT) with three outstanding plate bending elements (DKT, RDKTM and DST-BK), respectively, are used to study this phenomenon. Benchmark tests are implemented to evaluate the performance of three selected plate elements and the formulated flat shells.
Findings
The inter-element coupling effect of membrane and plate components belonging, respectively, to two adjacent shells deteriorate the performance of shells. Therefore, a shell’s performance cannot be guaranteed certainly by the superimposed membrane and plate behaviors.
Practical implications
The “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.
Originality/value
Previous studies mainly focus on formulation of high-performance membrane and plate elements. However, the inter-element coupling effect of membrane and plate components between two adjacent shells occurring on the common boundary, has attracted less attention. Thorough benchmark tests for three flat shells are implemented to investigate the phenomenon. The results shows that the inter-element coupling effect deteriorates the performance of shells. And the “order matching” criterion is proposed to explain this phenomenon and it is concluded that the flat shell that follows this criterion explicitly may alleviate or even overcome the inter-element coupling effect.
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Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Abstract
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
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Shi Zhang, Yun Zhang, Songxin Shi, Zhigao Huang and Huamin Zhou
– The purpose of this paper is to propose a new surface model combining the eccentric shell with multi-point constraint (MPC) for warpage prediction of injection molded plastics.
Abstract
Purpose
The purpose of this paper is to propose a new surface model combining the eccentric shell with multi-point constraint (MPC) for warpage prediction of injection molded plastics.
Design/methodology/approach
In this paper, three benchmark tests and a practical example are implemented to evaluate the performance of the new surface model and existing models.
Findings
The results demonstrate that the proposed model could give satisfactory solutions and has advantages over the existing models.
Practical implications
More precisely predicted warpage field for injection molded plastics can be achieved with the purposed model, such as that in the practical case.
Originality/value
The surface models are efficient and still popular for practical injection molding analysis. However, the existing models for warpage prediction cannot properly represent the true strain energy and obey material continuity assumption, and also they have not been assessed rigorously by benchmark tests. To overcome above-mentioned difficulty, a new surface model is proposed, which employs the eccentric shell without shear factor and MPC equation that ensuring material continuity. The results from experiment illustrate that the new model is superior to existing models.
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Bing Han, Tianze Chi, Fangjie Hu and Mengjun Wang
This paper divides the dyadic supply chain into three power structures according to the relative channel power of the supply chain members and consequently examines the optimal…
Abstract
Purpose
This paper divides the dyadic supply chain into three power structures according to the relative channel power of the supply chain members and consequently examines the optimal supply chain pricing decisions when both suppliers and retailers are concerned with fairness issues.
Design/methodology/approach
Three models are constructed, namely the Stackelberg game model with the supplier as the leader, the Nash game model with the balance of power and another Stackelberg game model with the retailer as the leader. The equilibrium solutions are solved, and their results are analyzed.
Findings
The retail price of a product increases with an increase in the fairness concerns of the leader in a supply chain in which the supplier or retailer is the leader, while the fairness concerns of the member with less channel power have no effect on the retail price. In a power-balanced supply chain, both suppliers and retailers increase their retail prices as their fairness concerns increase. The relative size of the members’ fairness concerns affects member profits and total supply chain profits.
Originality/value
The main contributions are as follows: First, this paper proposes a new approach to studying supply chain pricing strategy, considering fairness concerns and power structure. Secondly, three game models are constructed. The Nash equilibrium solution is introduced to study the fairness of supply chain participants in pricing decisions and overall supply chain profitability. Finally, the supply chain management theory is expanded by this study on pricing decisions and supply chain performance.
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Yanting Huang, Sijia Liu and Yuqing Liang
This paper aims to explore the effect of fairness concerns on supply chain members' optimal decisions and profits, to compare their profits under different policies, and to…
Abstract
Purpose
This paper aims to explore the effect of fairness concerns on supply chain members' optimal decisions and profits, to compare their profits under different policies, and to investigate the impact of each policy on members, consumers, and the environment with fairness concerns.
Design/methodology/approach
Considering government policies and fairness concerns in recycling management, this paper develops five recycling and remanufacturing decision models (anarchy policy model, reward-penalty mechanism model, recycling investment subsidies model, government tax model, and fund subsidy system model). In each model, the manufacturer and the online platform form the Stackelberg game. This research further discusses comprehensive environmental benefits and consumer surplus under five scenarios.
Findings
First, the fairness concerns of the online platform inhibit the recovery rate and supply chain members' profit while increasing the platform's utility. Second, fairness concerns increase the profit gap between the manufacturer and online platform, and the higher the degree of fairness concerns, the greater the profit gap; however, the four policies reduce the profit gap. Finally, when there are fairness concerns, environmental taxes damage the interests of supply chain members and consumers, but are most beneficial to the environment; recycling investment subsidies are on the contrary; the fund subsidy system depends on the relative size of the treatment fund and the subsidy fund.
Originality/value
This paper provides useful insights on how to regulate government policy to improve supply chain management with fairness concerns.
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Soumita Ghosh, Abhishek Chakraborty and Alok Raj
This study aims to examine how fairness concerns and power structure in dyadic green supply chains impact retail price, supply chain profits and greening level decisions.
Abstract
Purpose
This study aims to examine how fairness concerns and power structure in dyadic green supply chains impact retail price, supply chain profits and greening level decisions.
Design/methodology/approach
This study develops game-theoretic models considering fairness concerns and asymmetric power structures under an iso-elastic demand setting. The research paper employs the Stackelberg game approach, taking into consideration the fairness concern of the channel leader.
Findings
The findings indicate that under fairness, there is an increase in both wholesale and retail prices, as well as greening expenditures. Notably, when comparing the two models (manufacturer Stackelberg and retailer Stackelberg), double marginalization is more pronounced in the retailer Stackelberg setup than in the manufacturer Stackelberg setup. In a traditional supply chain with iso-elastic demand, the follower typically extracts higher profit compared to the leader; however, our results show that, under fairness conditions, the leader achieves higher profit than the follower. Additionally, our study suggests that supply chain coordination is unattainable in a fairness setup. This paper provides insights for managers on the optimal supply chain structure and the level of fairness to maximize profit.
Originality/value
This paper investigates the impact of a leader's fairness on the optimal decisions within a green supply chain, an area that has received limited attention previously. Additionally, the study investigates how fairness concerns manifest in distinct power dynamics, specifically, in the contexts of manufacturer Stackelberg and retailer Stackelberg.
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Abhay Kumar Chaubey, Ajay Kumar and Anupam Chakrabarti
This paper aims to present a new mathematical model for laminated rhombic conoids with reasonable thickness and depth. The presented model does not require the shear correction…
Abstract
Purpose
This paper aims to present a new mathematical model for laminated rhombic conoids with reasonable thickness and depth. The presented model does not require the shear correction factor, as transverse strain variation through the thickness was assumed as a parabolic function. The zero transverse shear stress provision at the bottom and the top of rhombic conoids was enforced in the model. The presented model implemented a C0 finite element (FE) model, eliminating C1 continuity requirement in the mathematical model. The proposed model was validated with analytical, experimental and other methods derived from the literature.
Design/methodology/approach
A novel mathematical model for laminated composite skew conoidal shells has been proposed. Parabolic transverse shear strain deformation across thickness is considered. FE coding of the proposed novel mathematical model was done. Slope continuity requirement associated with present FE coding has been suitably avoided. No shear correction factor is required in the present formulation.
Findings
This is the first attempt to study the bending response of laminated rhombic conoids with reasonable thickness and depth. After comparisons, the parametric study was performed by varying the skew angles, boundary conditions, thickness ratios and the minimum rise to maximum rise (hl/hh) ratio.
Originality/value
The novelty of the presented model is reflected by the simultaneous addition of twist curvature in the strain field as well as the curvature in the displacement field allowing the accurate analysis of reasonably thick and deep laminated composite rhombic conoids. The behavior of conoids differs from that of usual shells such as cylindrical and spherical due to the conoid’s inherent twist curvature with its complex geometry and different location of maximum deflection.
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Zixiang Hu, Zhenmin Wang, Shi Zhang, Yun Zhang and Huamin Zhou
The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to…
Abstract
Purpose
The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.
Design/methodology/approach
To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.
Findings
Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.
Originality/value
The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.