On the derivation of the transport equation for swelling porous materials with finite deformation

Deriving a physically meaningful transport equation for porous swelling materials that undergo finite deformations depends largely on our ability to relate thermodynamically defined variables to physically interpretable quantities. This article presents a novel and judicious choice of independent variables for the solid phase that clarifies the relationship between thermodynamically defined pressure and actual physical stress. Furthermore, it elucidates and simplifies the derivation of the transport equation previously investigated by [P.P. Singh, J.H. Cushman, D.E. Maier, Multiscale fluid transport theory for swelling biopolymers, Chemical Engineering Science 58(11) (2003) 2409–2419], while continuing to capture the important features. With this choice of variables, the assumptions and derivation of the transport equation are clarified. It is then shown how this framework can be used to derive a transport equation used to model swelling polymers. The result is compared with another transport equation derived using the Flory–Huggins theory.     

A derivation of the uniqueness conditions in coupled thermoplasticity

This article presents the proof of local and global uniqueness conditions in rate independent coupled thermoplasticity. The mathematical structure of rate equations which account for all coupling effects was discussed in [1] where uniqueness conditions were stated without proof and discussed for some particular cases.     

Thermodynamic derivation of dynamic boundary value problem and heat conduction equation for polarised thermoelastic materials

Summary It is shown that the dynamic boundary value problem and the heat conduction equation for simple piezoelectric materials with time-dependent properties result from the first and second law of thermodynamics. It is also shown that the conventional form of the heat conduction equation for geometrically nonlinear anisotropic thermoelastic media does not satisfy the principle of material frame indifference. A new form of the heat conduction equation is proposed.     

A practical rule for the derivation of transition finite elements

The derivation of shape functions of two‐dimensional regular and transition finite element using Pascal triangle concept is presented. A practical rule for the trial function selection from Pascal triangle is developed. The derived elements are tested using some case studies. The results are validated by ANSYS. The developed rule is also generalized for the three‐dimensional finite elements. Copyright © 2000 John Wiley & Sons, Ltd.     

A derivation of the underlying constructs of just-in-time management systems.

Researchers have recommended that the theoretical constructs underlying just-in-time (JIT) management systems be identified and developed if JIT is to be fully understood and its full capabilities realized. In this study, we advanced this conceptual development through an instrument based on the relevant literature and empirically deriving three underlying constructs: (1) operating structure and control, (2) product scheduling, and (3) quality implementation. We report a content analysis of these constructs and develop propositions regarding their relationships, predecessors, and outcomes.     

The derivation and validation of the practical operating equation for electromagnetic flowmeters: case of having an electrolytic conductor flowing through

In this paper, the practical operating equation for the electromagnetic flowmeter is derived for the case of having a circular pipe with an electrolytic conductor flowing through. It is assumed further that the magnetic field is uniform and the velocity profile is axisymmetric (assuming nonconducting walls). The derivation was done before by many authors to whom the author refer to in this paper, but the approach provided here is comprehensive and simple. To add to that, the solution for the electromagnetic flowmeter's operating equation illustrated in this paper is new and is provided using very simple mathematical concepts, eliminating the complexity of solutions provided by other authors in the past. In the end, the practical operating equation derived was validated using a new approach based on the finite element analysis and the moving stream method to estimate the error resulting from using this operating equation with the assumptions of having a uniform magnetic field and an axisymmetric velocity profile, which are difficult to achieve in practice. This error can be used in a dry calibration to estimate the error caused by variable flow characteristics.     

A solution of the diffusion equation

A nonstationary solution is obtained for the diffusion equation in the case of two gas containers of arbitrary volume, connected by a capillary. If the volume of the capillary is regarded as negligibly small in comparison with the flask volumes, the solution turns into the formula derived by Ney and Armsteady, and as the volume of one of the flasks approaches infinity, the solution turns into the one derived by Frank-Kamenetskii.     

A virtual work derivation of the scaled boundary finite-element method for elastostatics

 The scaled-boundary finite element method is a novel semi-analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. This paper develops a new virtual work formulation and modal interpretation of the method for elastostatics. This formulation follows a similar procedure to the traditional virtual work derivation of the standard finite element method. As well as making the method more accessible, this approach leads to new techniques for the treatment of body loads, side-face loads and axisymmetry that simplify implementation. The paper fully develops the new formulation, and provides four examples illustrating the versatility, accuracy and efficiency of the scaled boundary finite-element method. Both bounded and unbounded domains are treated, together with problems involving stress singularities. Received 20 May 2001 / Accepted 1 February 2002     

A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation

An integral equation method is presented for the numerical calculation of the eigenvalues of the scalar Helmholtz equation. By using a particular solution instead of Green's function, the calculations could be simplified due to the elimination of complex numbers.     

A direct derivation of the equations of motion for 3D-flexible mechanical systems

Equations of motion for rigid bodies with the body-fixed co-ordinate system placed at or away from the centre of mass are derived in a clear and direct way by making use of the two basic equations of mechanics (Newton's second law and the corresponding law of angular momentum). The dynamic equations for flexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straightforward manner, because this principle treats inertia as a force. The flexible formulation is exemplified by the use of circular beam elements and some basic matrices are derived in a direct way using skew-symmetric matrices. The capabilities of the formulation are demonstrated through examples. Results are compared with and verified by examples from the literature. Derivations throughout the paper are simplified by means of skew-symmetric matrices. © 1998 John Wiley & Sons, Ltd.     

Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: a microphysical derivation from statistical electromagnetics

The concepts of statistical electromagnetics are used to derive the general radiative transfer equation (RTE) that describes multiple scattering of polarized light by sparse discrete random media consisting of arbitrarily shaped and arbitrarily oriented particles. The derivation starts with the volume integral and Lippmann-Schwinger equations for the electric field scattered by a fixed N-particle system and proceeds to the vector form of the Foldy-Lax equations and their approximate far-field version. I then assume that particle positions are completely random and derive the vector RTE by applying the Twersky approximation to the coherent electric field and the Twersky and ladder approximations to the coherency dyad of the diffuse field in the limit N --> infinity. The concluding section discusses the physical meaning of the quantities that enter the general vector RTE and the assumptions made in its derivation.     

Phenomenological derivation of the Onsager reciprocal relations

The Onsager reciprocal relation for a linear dissipative system with two fluxes is derived within the framework of a phenomenological approach using the property of nonnegative definiteness of the dissipative function. It is established that the Onsager relations are valid when the generalized fluxes are zero for nonzero generalized thermodynamic forces. In the general case, the Onsager reciprocal relations can be phenomenologically derived based on the theory of matrices and determinants or on the Prigogine principle of the entropy production minimum.     

A cartesian-tensor solution of the Brinkman equation

A method of solving the Brinkman equation, using Cartesian tensors, is developed. General expressions for the velocity vector and the pressure, which can directly be used in situations where boundary conditions are expressible in Cartesian-tensor form, are obtained. It is shown how the drag on a porous sphere can be directly and easily calculated using this method.     

A rigorous derivation for T-stress in line crack problem

In this paper, a rigorous derivation for T-stress in line crack problem is presented. Similar to the edge crack case, this paper provides the T-stress dependence on loading with the Dirac delta function property.