A new formulation and computation of the triphasic model for mechano-electrochemical mixtures

From the generalized first law of thermodynamics for an irreversible thermodynamical system, a new set of governing equations for the mixture theory is derived based on the triphasic model for mechano-electrochemical mixtures. It is shown that, in the case of electroneutral solution, a new biphasic mixture theory including the electrochemical effects can be derived from the new governing equations. The chemical-expansion stress representing both the influences of deformation on the fixed charge density and the electric potential of fixed charge field is given. For comparison and verification purposes, the numerical solution for a confined compression problem of a charged hydrated soft tissue is computed using the multiquadric method. Received: 1 November 1998     

Middle-field formulation for the computation of wave-drift loads

New formulations of second-order wave loads contributed by a first-order wave field are developed by applying two variants of Stokes’s theorem and Gauss’s theorem to a formulation consisting of direct pressure integrations on a body’s hull which is called the near-field formulation. In addition to this direct formulation and the formulation derived from the momentum theorem called the far-field formulation, for the computation of drift (surge/sway) forces in horizontal directions and drift (yaw) moment around the vertical axis, one of new formulations is defined on the control surfaces surrounding the body and called the middle-field formulation. After a brief summary of both pressure-integration (near-field) and momentum (far-field) formulations, the development of the middle-field formulation involving control surfaces is described and complemented in detail in the appendices. The application of the new formulation shows that the near-field and far-field formulations are mathematically equivalent for wall-sided, as well as non-wall-sided bodies and under the condition that the mean yaw moments are expressed with respect to a space-fixed reference point. It is shown that the middle-field formulation is as robust as the far-field formulation and as general as the near-field formulation of second-order loads on a single body as well as on multiple bodies. Furthermore, the extension to the computation of a second-order oscillatory load, which is so far accessed only by the near-field formulation, is envisioned.     

流线型回转体外形设计综述与线型拟合

综述了流线型回转体外形设计的主要方法：(1)具有精确数学表达式的几何组合外形曲线；(2)用源汇法设计回转体外形曲线；(3)用离散外形坐标型值表示的回转体线型。给出了流线型离散型值回转体线型的拟合解析表达式。这些外形设计方法与拟合解析表达式具有广泛的工程实用价值。     

A mathematical formulation for interface-based modular product design with geometric and weight constraints

Since customer preferences change rapidly, there is a need for design processes with shorter product development cycles. Modularization plays a key role in achieving mass customization, which is crucial in today's competitive global market environments. Standardized interfaces among modularized parts have facilitated computational product design. To incorporate product size and weight constraints during computational design procedures, a mixed integer programming formulation is presented in this article. Product size and weight are two of the most important design parameters, as evidenced by recent smart-phone products. This article focuses on the integration of geometric, weight and interface constraints into the proposed mathematical formulation. The formulation generates the optimal selection of components for a target product, which satisfies geometric, weight and interface constraints. The formulation is verified through a case study and experiments are performed to demonstrate the performance of the formulation.     

The mathematical formulation for the event sequence diagram framework

The Event Sequence Diagram (ESD) framework allows modeling of dynamic situations of interest to PRA analysts. A qualitative presentation of the framework was given in an earlier article. The mathematical formulation for the components of the ESD framework is described in this article. The formulation was derived from the basic probabilistic dynamics equations. For tackling certain dynamic non-Markovian situations, the probabilistic dynamics framework was extended. The mathematical treatment of dependencies among fault trees in a multi layered ESD framework is also presented.     

An enhanced Lemaitre model formulation for materials processing damage computation

The Lemaitre damage model is now widely used to deal with coupled damage analyses for various mechanical applications. In this article, different extensions of the model are presented and discussed to deal with complex multiaxial configurations—such as multi-stages bulk forming processes. A specific treatment is done to account for compressive damage growth, and a stress triaxiality cut-off value is considered to avoid any damage evolution below a critical negative triaxiality. The damage potential is also modified to deal with highly ductile materials, and the plastic strain is split into a negative part and a positive part to differentiate damage growth for compressive states of stress and for tensile states of stress. Finally, an anisotropic damage approach based on the comparison between grain flow orientation and principal loading directions is defined. A combination of these extensions is achieved within a single Lemaitre formulation. Application on different examples show the robustness and accuracy of the model defined in this paper.     

Effects of numerical formulation on magnetic field computation using meshless methods

Meshless methods have some advantages over their counterparts such as the finite-element method (FEM). However, existing meshless methods for computational electromagnetic fields are still not as efficient as FEM. In this paper, we compare two meshless methods of discretizing the computational domain of Poisson-like problems; namely, the point collocation and Galerkin methods (which use the strong and weak forms of the governing equation respectively), and their effects on the computational accuracy and efficiency of the magnetic fields. We also discuss methods of handling discontinuities at the material interface. We present several examples, which also provide a means to validate and evaluate both meshless methods. Exact solutions and/or FEM are used as a basis for comparison. In addition, we also verify the results by comparing computed magnetic forces against those measured experimentally.     

Integral formulation for large-scale eddy current computation of a Superconducting magnet system

The eddy currents' distribution is investigated during a transient process in a superconducting magnet system. We have applied a numerical method based on an integral approach. In such a method, only the coils of the magnet system without the air embedding are discretized. Such integral approach leads to the full matrices and consequentially to large computational requirements. There are techniques, which generate less dense matrices by introducing groups of long-range interactions. We have applied a similar technique based on equivalent currents in the coils.     

A unified mathematical programming formulation of strain driven and interior point algorithms for shakedown and limit analysis

A mathematical programming formulation of strain‐driven path‐following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in an FEM context is presented. From the optimization point of view, standard arc‐length strain‐driven elastoplastic analyses, recently extended to shakedown, are identified as particular decomposition strategies used to solve a proximal point algorithm applied to the static shakedown theorem that is then solved by means of a convergent sequence of safe states. The mathematical programming approach allows: a direct comparison with other non‐linear programming methods, simpler convergence proofs and duality to be exploited. Owing to the unified approach in terms of total stresses, the strain‐driven algorithms become more effective and less non‐linear with respect to a self‐equilibrated stress formulation and easier to implement in the existing codes performing elastoplastic analysis. The elastic domain is represented avoiding any linearization of the yield function so improving both the accuracy and the performance. Better results are obtained using two different finite elements, one with a good behavior in the elastic range and the other suitable for performing elastoplastic analysis. The proposed formulation is compared with a specialized implementation of the primal–dual interior point method suitable to solve the problems at hand. Copyright © 2011 John Wiley & Sons, Ltd.     

A new formulation of operation allocation problem in flexible manufacturing systems: mathematical modelling and computational experience

This paper extends the formulation of the operation allocation problem to include the important planning aspects of refixturing and limited tool availability. A 0–1 integer programming formulation is proposed with two objective functions and a set of realistic constraints. The computational behavior of the solution is discussed and a number of observations prompted by the solution methodology have been made.     

Numerical computation of internal stress and velocity in time-domain¶bem formulation for elastodynamics

 This work is concerned with the computation of space and time derivatives (scalar wave) and stress and velocity components (elastodynamics) in a time-domain BEM formulation. Two approaches are presented: the first employs standard closed form integral equations related to desired variables, the second is based on a procedure that employs numerical derivatives of the basic boundary integral equation. In the latter, the kernels are written as functions of source point complex co-ordinates and the derivatives are computed, numerically, taking only the imaginary part. Both approaches produce reliable results, as demonstrated by three examples. Received: 4 June 2002 / Accepted: 16 September 2002     

Restructuring the Indian agro-fresh food supply chain network: a mathematical model formulation

Clean Technologies and Environmental Policy - In traditional Indian agro-fresh food supply chain (AFSC), authors identify the following four shortcomings through the literature survey: (1)...     

Application of mathematical modeling for the development and optimization formulation with bioactive copper complex

New formulation for treatment a copper deficiency in human organism was developed and optimized by application of mathematical modeling. This formulation contained copper (II) complex with polysaccharide pullulan, as active substance. The binder concentration [polyvinyl pyrrolidone (PVP %)], the disintegrant concentration (corn starch %) and the resistance to crushing (hardness) were taken as independent variables. In vitro measured drug release characteristics of the tablets at pH 1.20 and 7.56 were studied as response variables. Initially, the created full factorial 2³ model showed that the resistance to crushing has the most significant effect on copper (II) complex release from the formulation. Optimal tablet formulation F2, with lower Hardness (50 N), lower Starch (20.0%) and higher PVP (2.7%) concentrations, is selected using the partial least squares (PLS) regression modeling. The selected formulation F2 has expressed the best drug release profile at both pH (98.66% pH = 1.20; 93.35% pH = 7.56), and the lowest variation of tablets weight. The presented theoretical approach and created PLS model can be readily applied in future copper complexes studies and formulation design.     

A mathematical formulation and anarchic society optimisation algorithms for integrated scheduling of processing and transportation operations in a flow-shop environment

This paper addresses a permutation flow-shop scheduling problem where there are a finite number of transporters to carry jobs from each machine to its subsequent machine. The problem is first formulated as a mixed-integer linear programme, and then two anarchic society optimisation (ASO) algorithms are developed to solve large-sized instances of the problem. The numerical experience shows that the ASO algorithms are considerably effective and efficient. Finally, a sensitivity analysis is carried out to study the performance of the manufacturing system versus the transportation times and the number of transporters.     

A mathematical model of saltation

Summary This paper presents a model of the uplift by wind of heavy (i.e. saltating and unaffected by turbulent diffusion) soil particles. Detailed trajectories are not calculated, although trajectory heights are required and this necessitates taking account of the drag on particles. Quantities required as input are (a) the mass-concentration at a height equal to the roughness length above the surface for each size class, (b) the roughness length of the undisturbed surface, and (c) the friction velocity which is assumed to be controlled by the overlying wind and unaffected by erosion. The model is combined with a previously bublished model for lighter particles and applied to hypothetical size distributions for a range of friction velocities. Mean-diameter profiles and horizontal fluxes are obtained and found to agree well with observations by various workers.