Let G be a finite group. A subset X of G is a set of pairwise non-commuting elements if any two distinct elements of X do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic 2-group and in any finite non-abelian p-group with an abelian maximal subgroup.

This study introduces a finite element method using a higher-order interpolation function for effective simulations of wave transformation. Finite element methods with a higher-order interpolation function usually employ a Lagrangian interpolation function that gives accurate solutions with a lesser number of elements compared to lower order interpolation function. At the same time, it takes a lot of time to get a solution because the size of the local matrix increases resulting in the increase of band width of a global matrix as the order of the interpolation function increases. Mass lumping can reduce computation time by making the local matrix a diagonal form. However, the efficiency is not satisfactory because it requires more elements to get results. In this study, the Legendre cardinal interpolation function, a modified Lagrangian interpolation function, is used for efficient calculation. Diagonal matrix generation by applying direct numerical integration to the Legendre cardinal interpolation function like conducting mass lumping can reduce calculation time with favorable accuracy. Numerical simulations of regular, irregular and solitary waves using the Boussinesq equations through applying the interpolation approaches are carried out to compare the higher-order finite element models on wave transformation and examine the efficiency of calculation.

After the Northridge earthquake, special concentrically braced frames (SCBF) have recently been introduced; further studies conducted to eliminate their shortcomings, design flaws and implementation of connector plates and their vague behavior after seismic load cycles led to development of a new CBF called buckling restrained braced frame (BRBF). In these braces, the steel core which is enclosed within steel profile filled by special concrete encloses the core completely and prevents buckling and increased critical load until compressive axial capacity is only restrained by steel yield tension. This allows the steel core resist against axial forces using entire resistance of the steel as long as casing resists against tensile buckling. As a result, braces act as structural fuse and lead to plastic behaviors, beams, and columns remain elastic in the seismic process. This study builds, tests and numerically models a buckling restrained brace to evaluate sample adequacy to meet requirements of the AISC 341-16 code.

Modifying stress-strain curves is one of the important topics in mechanical engineering and materials science. Real stress-strain curves should be modified after necking point as stress becomes three-dimensional after creation of throat, and consequently, equivalent stress should be used instead of axial one. Also, distribution of triple stresses across throat section is not uniform anymore, and it is not possible to calculate the stress through dividing force value by surface area. Methods presented to modify these curves mainly have some defects which enter the error resulting from simplifying assumptions into the results. Entrance of stress analysis softwares into mechanical engineering has caused use of finite elements methods in order to modify stress-strain curves. As you know, being as an input for stress analysis software, as one of the applications of these curves, has a direct effect on simulation results. Optimization methods have been developed and extended in engineering sciences. Modifying stress-strain curves may be an application of these methods. Considering the sample shape resulting from tension test as the basis in this research, we have changed the modified stress-strain curved in a way that the shape resulting from simulation coincides with the sample resulting from the test. Accordingly, the stress-strain curve has been modified, and the results have been verified, using results obtained from normal methods such as Bridgeman method.

After the Northridge earthquake, special concentrically braced frames (SCBF) have recently been introduced; further studies conducted to eliminate their shortcomings, design flaws and implementation of connector plates and their vague behavior after seismic load cycles led to development of a new CBF called buckling restrained braced frame (BRBF). In these braces, the steel core which is enclosed within steel profile filled by special concrete encloses the core completely and prevents buckling and increased critical load until compressive axial capacity is only restrained by steel yield tension. This allows the steel core resist against axial forces using entire resistance of the steel as long as casing resists against tensile buckling. As a result, braces act as structural fuse and lead to plastic behaviors, beams, and columns remain elastic in the seismic process. This study builds, tests and numerically models a buckling restrained brace to evaluate sample adequacy to meet requirements of the AISC 341-16 code.