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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

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.

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.

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.

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.

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.

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.

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.

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.

In this paper, three benchmark tests and a practical example are implemented to evaluate the performance of the new surface model and existing models.

The results demonstrate that the proposed model could give satisfactory solutions and has advantages over the existing models.

More precisely predicted warpage field for injection molded plastics can be achieved with the purposed model, such as that in the practical case.

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.

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.

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.

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.

This paper provides useful insights on how to regulate government policy to improve supply chain management with fairness concerns.

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.

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.

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.

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.

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.

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.

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.

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.

As one of the omnichannel sales models, “buy online and pick up in store” (BOPS) not only is used in the commercial field but also has gradually attracted many scholars’ interests. However, although there are numerous research ideas, most of the current work is still limited to theoretical and empirical research, and few scholars study BOPS through models. This paper aims to discuss the best market conditions and opportunities for the implementation of BOPS against the backdrop of omnichannel by means of mathematical models and data simulations and discuss the optimal price–service strategies under different sales models.

First, from the perspective of different consumer shopping types, this paper separately divides consumers into different groups in traditional “dual channel” and BOPS models. Then, the authors analyze the impact of company market size, consumer service sensitivity and the scale of BOPS on companies’ strategies and the profit of the supply chain. Subsequently, they conduct an empirical analysis through specific values. Finally, the authors further expand the model on the basis of the original research, and discuss the retailer’s fairness concerns and unit compensation strategy to ensure that the research content is more rigorous.

It is observed that whether companies adopt BOPS depends on consumers’ service sensitivity degree and the scale of BOPS consumers and online retailers: when the sensitivity and the proportion of online consumers are high or the number of BOPS consumers is large, it is more advantageous for companies to implement BOPS. Moreover, companies should not only consider the market scale and production cost but also have a precise orientation of consumers’ experience sensitivity and willingness to engage in extra consumption when making price and service strategies. At the same time, the compensation strategy of companies and the peer-regarding fairness concern behavior of offline retailers will affect the optimal price and service strategy in the BOPS model.

These results provide managerial insights for companies preparing to implement BOPS and promote the development of relevant theories in the channel field.

At present, most of the research on BOPS is based on empirical reviews. However, this paper analyzes the applicability and feasibility of implementing BOPS by using specific models, and it will provide some reference for companies preparing to implement BOPS. In addition, this paper also discusses the unit compensation strategy and peer-regarding fairness concern behavior in the BOPS model, which have not been studied by relevant scholars.