Enriched Finite Element for Modelling Variable Boundary Conditions in Unsaturated Seepage Problems

Partial differential equations such as models for flow in unsaturated porous media are difficult to be solved when space-time variable boundary conditions are included. A general solution to this problem is discussed in this contribution and is devised in such a way that the face with variable boundary condition can be subjected to Dirichlet, Neumann or the so-called Signorini/ambiguous boundary conditions, considering the transition from one type to another. A method based on the enrichment of finite elements that is able to accurately model seepage with these complex boundary conditions is discussed. Simulations are presented illustrating the capabilities of the new method in 2D and 3D, including cases where the free surface varies due to rain.

Transient Numerical Simulation of Linear Thermal Transmittance in Software CalA

Calculation of heat losses of buildings according to European standard EN ISO 10211 and Czech standard ČSN 73 0540 is simplified to one-dimensional time-steady heat conduction through the building construction in direction of the largest temperature gradient. This simplification of the calculation is incorrect in case of complex geometry. Calculation according to norm takes into account this inaccuracy and uses Linear Thermal Transmittance Ψ [W/(m·K)] in 2D geometry or Point Thermal Transmittance χ [W/(m2·K)] in the 3D geometry as a calculation correction. This contribution is focused on detailed calculation of linear thermal transmittance in case of contact external peripheral wall and plastic window frame. Results of two-dimensional transient numerical simulation show unsteady linear thermal transmittance in time and dependence on solar radiation. All of these variable boundary conditions can be easily simulated in the software CalA as well as complex geometry.

Analysis of Polymer Micro Fibers: A Smoothed Particle Hydrodynamics Approach

The nanofibrillar array of a Gecko inspired Synthetic Adhesive (GSA) adheres to a surfaces when fibers undergo deformations of both the stems and the tip. The GSA’s show interesting changes in effectiveness dependent on use patterns, preloads, and material types, amongst other parameters. The polymers fibers also, display plastic creep even at relatively low strain rates and stresses below plastic yield. Therefore, a suitable numerical solution, which predicts the fiber geometry, must consider not only the initial shape of the fiber, but also the fiber progressive deformation (local and global) and the influence this has on the local mechanical properties (elastic, viscoelastic, strain hardening/softening and plastic flow). The localized mechanical properties are difficult to calculate using traditional methods because of the nonlinearities associated with viscoelastic effects, the large deformations, and the variable boundary conditions. However, the variable boundary conditions make a mesh free modeling method ideal. Smooth Particle Hydrodynamics (SPH) is one of the most prominent mesh free Lagrange method, which takes a set particle and uses particle kinematics, density gradients, and material properties to determine the interaction between particles. As a first step towards modeling the behavior of a fibrillar adhesive surface, this paper focuses on the modeling of a single polymer fiber. The single micro fiber will be subjected to similar conditions to what it would see as part of an array. This will allow the SPH method of simulation to be critiqued for its further use in simulating polymer microfiber. While the localized mechanical properties of the polymer, which depend on viscoelastic effect and other nonlinear phenomena, are difficult to determine analytically. The modeling technique can be compared to standard analytical methods for global parameters. It was found that the SPH method was able to appropriately model the effect of various scenarios on the mechanical deformation and resonance of a polymer microfiber. Further more the friction force for the fiber on glass was calculated as were the localized fiber velocities and stresses.

The homogenization of elliptic partial differential systems on rugous domains with variable boundary conditions

This paper is devoted to studying the asymptotic behaviour of a sequence of elliptic systems posed in a sequence of rough domains Ωn. The solutions un are assumed to satisfy un(x) ϵ Vn(x), where Vn(x) is a vectorial space depending on $\smash{x\in\bar\varOmega_n}$. This enables one to consider several types of boundary conditions posed in variable sets of the boundary. For some choices of the vectorial spaces Vn(x), our study provides, in particular, some classical results for the homogenization of Dirichlet elliptic problems in varying domains.