ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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Recently Published Articles
- The study of fluid flow and heat transfer of a viscous incompressible fluid between a rotating solid disk and a stationary permeable disk using the Brinkman-Darcy model
Dayle C. Jogie and Balswaroop Bhatt
Article first published online: 2 JUL 2015 | DOI: 10.1002/zamm.201400089
The study of momentum and heat transfer has been carried out for the case of a viscous incompressible fluid between a rotating solid and a stationary permeable disk, whose depth is equal to that of the free fluid. Navier-Stokes equations govern the flow in the free fluid, while the flow in the porous region is governed by a combination of Brinkman and Darcy equations, respectively. Energy equations in the free fluid region and the porous region have been considered. A two step numerical process is employed; series expansions are first created to give analytical approximations of momentum and energy equations in MAPLE, while a Runge-Kutta algorithm bvp4c is then employed in MATLAB to numerically evaluate the velocity and temperature distributions in the flow fields. Velocity profiles, temperature profiles and relevant streamlines are sketched for various models involving variations in parameters such as Reynolds number, Brinkman number, and Prandtl number. It is observed that various parameters have differing effects on associated profiles which are subsequently discussed in the paper.
- Energy conservation and dissipation properties of time-integration methods for nonsmooth elastodynamics with contact
Article first published online: 1 JUL 2015 | DOI: 10.1002/zamm.201400231
This article is devoted to the study of the conservation and the dissipation properties of the mechanical energy of several time–integration methods dedicated to the elasto–dynamics with unilateral contact. Given that the direct application of the standard schemes as the Newmark schemes or the generalized–α schemes leads to energy blow-up, we study two schemes dedicated to the time–integration of nonsmooth systems with contact: the Moreau–Jean scheme and the nonsmooth generalized–α scheme. The energy conservation and dissipation properties of the Moreau–Jean is firstly shown. In a second step, the nonsmooth generalized–α scheme is studied by adapting the previous works of Krenk and Høgsberg in the context of unilateral contact. Finally, the known properties of the Newmark and the Hilber–Hughes–Taylor (HHT) scheme in the unconstrained case are extended without any further assumptions to the case with contact.
- Strategies for stiffness analysis of laminates with microdamage: combining average stress and crack face displacement based methods
Article first published online: 29 JUN 2015 | DOI: 10.1002/zamm.201400296
Many approximate analytical models have been developed to calculate stress state between intralaminar cracks with the aim to predict the degradation of certain elastic property (most often axial modulus or shear modulus) of cross-ply laminate. Often they are plane stress solutions and laminate constants like Poisson's ratios cannot be considered. On the other hand the so called GLOB-LOC approach, presented in WWFE III, allows calculation of any thermo-elastic property of a general symmetric laminate with an arbitrary number of cracks in each layer provided that two local parameters – average and normalized crack opening displacement (COD) and crack face sliding displacement (CSD) are known. In this paper relationships are derived expressing these two parameters (COD and CSD) with average value of transverse stress and in-plane shear stress perturbation between cracks. Expressions are exact and independent on the approximations in the stress model. As examples, average perturbation functions for two shear lag models and Hashin's variational model are used to calculate damaged laminate properties that would not be available in original formulation: Poisson's ratio and thermal expansion coefficients. Predictions are compared with test data for GF/EP laminates and with more accurate predictions based on FEM calculations.
- Modeling and experimental investigations of elastic and creep properties of thermoplastic polymer nanocomposites
Jānis Zicāns, Remo Merijs Meri, Mārtiņš Kalniņš, Roberts Maksimovs and Juris Jansons
Article first published online: 25 JUN 2015 | DOI: 10.1002/zamm.201400288
The study is devoted to prediction of elastic and creep properties of thermoplastic polymer nanocomposites reinforced with anisodiametric nanoadditives (either carbon nanotubes, CNTs, or montmorillonite clay, MMT) by considering structural hierarchy of the nanocomposites and the nanofillers itself. The nanocomposites analysed have been based on both synthetic and biodegradable thermoplastic polymer matrices (polyethylene, PE, and plasticized starch, PS, respectively) with potential applications in packaging, building/construction and energetics. It has been demonstrated that modulus of elasticity, stress at break as well as stress at yield of the investigated polymer nanocomposites significantly increase upon introduction of a minor amounts of the aforementioned nanofillers into the polymer matrices. Gain in the modulus of elasticity of the investigated PS based nanocomposites has been described by applying the algorithm of stage-by-stage calculation of the elastic constants of the multiphase-systems containing anisodiametric plate-like nanoparticles with complex structure. Change of the modulus of elasticity of the investigated PE based nanocomposites has been described by applying the theoretical model based on micromechanics approach in consideration of distribution quality of CNTs within the polymer matrix. Creep resistance of neat PE and its nanocomposites in the investigated time frame has been described according to the Findley power law, in spite of the fact, that addition of CNTs increases creep rate to some extent, being the consequence of the nanofiller effect on both crystallinity degree of the polymer matrix as well as viscoelastic properties in the interfacial regions.
- Deformations near an elliptical hole with surface effect in a laminated anisotropic thin plate
Xu Wang and Peter Schiavone
Article first published online: 25 JUN 2015 | DOI: 10.1002/zamm.201400271
This work is concerned with the coupled stretching and bending deformation around an elliptical hole with surface energy in a laminated and inhomogeneous anisotropic elastic thin plate within the context of the Kirchhoff theory. A closed-form full-field solution is derived by using the octet formalism recently developed by Cheng and Reddy (2002, 2003, 2004, 2005) and by incorporating a simplified version of the surface elasticity model. In particular, explicit real-form expressions of the hoop membrane stress resultant, hoop bending moment, in-plane displacements and slopes on the mid-plane along the edge of the elliptical hole are obtained.