The initial post-buckling behaviour of a cold-formed channel member flange after its local buckling is investigated. An axially compressed column or beam subjected to pure bending is considered. The member material is assumed to follow a linear stress-strain relationship. The governing non-linear differential equation of the problem is derived using the minimum total potential energy principle. An approximate solution for the equation is found by means of the perturbation approach, which allows obtaining the critical buckling stress and the initial post-buckling equilibrium path. The bifurcation point is shown to be symmetric and stable. The proposed analytical solution is compared with finite element method (FEM) and finite strip method (FSM) results to check the validity and range of applicability.
The statistical impact of experimental result scatter of asphalt mixtures on their numerical modelling
The paper presents selected test results of asphalt mixture conducted in low temperatures. The obtained parameters are highly diverse. It concerns ultimate breaking loads, stiffness parameters related to Young's modulus but also the fracture course. Statistical analysis upon the results makes it possible to relevantly estimate the material-defining parameter values. Such a random approach leads to the mean values of breaking and fracture-triggering loads, dealing with their dispersion too. The estimated parameters allow to form appropriate numerical models of asphalt mixture specimens. This type of analysis supports the laboratory tests. The paper presents the authors' simplified model considering non-uniform material features. The results reflect the scatter of real laboratory test outcomes. In order to do so an algorithm to calibrate the numerical model parameters was created.
The study makes an attempt to model a complete vibrating guitar including its non-linear features, specifically the tension-compression of truss rod and tension of strings. The purpose of such a model is to examine the influence of design parameters on tone. Most experimental studies are flawed by uncertainties introduced by materials and assembly of an instrument. Since numerical modelling of instruments allows for deterministic control over design parameters, a detailed numerical model of folk guitar was analysed and an experimental study was performed in order to simulate the excitation and measurement of guitar vibration. The virtual guitar was set up like a real guitar in a series of geometrically non-linear analyses. Balancing of strings and truss rod tension resulted in a realistic initial state of deformation, which affected the subsequent spectral analyses carried out after dynamic simulations. Design parameters of the guitar were freely manipulated without introducing unwanted uncertainties typical for experimental studies. The study highlights the importance of acoustic medium in numerical models.
We consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the throughthe-thickness procedure applied to a 3D shell-like body.
Abdominal prostheses are used in humans for abdominal wall strengthening or reconstruction. From the mechanical point of view they are membranes, so their basic mechanical property is tensile stiffness. This property is experimentally identified for a selected implant, OptomeshTM. The obtained results are described herein. Uni-axial simple and cyclic tension tests are a basis for the analysis. Both kinds of tests allowed to distinguish two states of the material, namely: baseline and preconditioned. In the preconditioned state the material reveals approximate two-fold increase of tensile stiffness in comparison to baseline state. In both states the material demonstrate orthotropy. Both features are typical for knitted synthetic abdominal implants, however, the first one is not, while the other is desired from the mechanical point of view of operated hernia.