999 resultados para Beam equation
Resumo:
The LiteSteel beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSBs are commonly used as flexural members in buildings. However, the LSB flexural members are subjected to lateral distortional buckling, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist, and cross sectional change due to web distortion. An experimental study including more than 50 lateral buckling tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. It included the available 13 LSB sections with spans ranging from 1200 to 4000 mm. Lateral buckling tests based on a quarter point loading were conducted using a special test rig designed to simulate the required simply supported and loading conditions accurately. Experimental moment capacities were compared with the predictions from the design rules in the Australian cold-formed steel structures standard. The new design rules in the standard were able to predict the moment capacities more accurately than previous design rules. This paper presents the details of lateral distortional buckling tests, in particular the features of the lateral buckling test rig, the results and the comparisons. It also includes the results of detailed studies into the mechanical properties and residual stresses of LSBs.
Analytical Solution for the Time-Fractional Telegraph Equation by the Method of Separating Variables
Resumo:
We present a mass-conservative vertex-centred finite volume method for efficiently solving the mixed form of Richards’ equation in heterogeneous porous media. The spatial discretisation is particularly well-suited to heterogeneous media because it produces consistent flux approximations at quadrature points where material properties are continuous. Combined with the method of lines, the spatial discretisation gives a set of differential algebraic equations amenable to solution using higher-order implicit solvers. We investigate the solution of the mixed form using a Jacobian-free inexact Newton solver, which requires the solution of an extra variable for each node in the mesh compared to the pressure-head form. By exploiting the structure of the Jacobian for the mixed form, the size of the preconditioner is reduced to that for the pressure-head form, and there is minimal computational overhead for solving the mixed form. The proposed formulation is tested on two challenging test problems. The solutions from the new formulation offer conservation of mass at least one order of magnitude more accurate than a pressure head formulation, and the higher-order temporal integration significantly improves both the mass balance and computational efficiency of the solution.