Buckling capacity of functionally graded beams: A comparative study of different shear deformation beam theories

This paper investigates the postbuckling response of simply supported functionally graded beams under axial loading using several beam theories; classical beam theory, CBT, Timoshenko beam theory, TBT and parabolic shear deformation beam theory, PSDBT. Hamilton’s principle is used to derive the governing equations which are solved by closed-form method. It is assumed that the Young’s modulus is varying continuously in the thickness direction according to power-law form while all other material properties are taken to be constant. The effects of the reinforcement distribution, the beam edge-to-thickness ratio and the phase contrast (ratio of the reinforcement Young’s modulus to the matrix Young’s modulus) on the postbuckling behavior and critical buckling load of functionally graded beam are studied. Results demonstrate the important contribution of the shear effect to both the buckling and postbuckling behaviors. Finally, the combinations of reinforcement distribution, beam edge-to-thickness ratio and phase contrast that correspond to the highest and the lowest buckling capacities are identified.

Different operation regimes of cylindrical triode-type electron accelerator studied by PIC code simulations

The performance of the converging electron beam generated in cylindrical triodes is systematically studied by particle-in-cell code simulations. Depending on the cathode and grid potentials applied, different operation regimes are identified. For low voltages between cathode and grid, laminar flow and homogeneous beam energy density at the target (anode) is obtained. This applies both to the case of unipolar electron flow and to bipolar flow with counter-streaming ions. Hereby, the electron emission current is enhanced by about 50% for bipolar flow compared with unipolar flow. A further increase by about 20% is obtained when electron backscattering at the target is enhanced due to a change of target material from aluminum to tungsten. For cathode-grid voltages exceeding a critical value, laminar flow is replaced by non-laminar flow regimes. For unipolar electron beams, a virtual cathode forms between grid and target, which leads to an inhomogeneous power density at the target. For the specific geometry investigated and the cathode potential fixed at −120 kV, the cathode-grid voltage threshold for the formation of the virtual cathode is ~32 kV for Al targets and ~28 kV for W targets. For bipolar flow, the laminar flow regime already ends at cathode-grid voltages of ~23 kV (Al target) and ~20 kV (W target), respectively, and is replaced by magnetic insulation at the beam edge. For increasing cathode-grid voltage, the magnetically insulated region extends until beam pinching occurs.

Prestressed Concrete Beam Bridge Design and Main Parameters of Prestressed Steel Beam Calculations and Arrangement

Prestressed concrete beam bridge cross-section using T-shaped cross-section. Anti-shrinkage reinforcement requirements adopted under the dense arrangement of all the memorial steel welds are double-sided welding, using a special form of prestressed reinforcement arranged in assembly is completed, tension on the deck to prevent the beam edge cracking.

Numerical Analysis of the Effect of Phase Transformation on Residual Stresses in an Autogenous Beam Edge Weld

This paper presents the numerical analysis of phase proportions and residual stresses in an autogenous beam edge weld. The thin beam was welded running a heat source along its longer edge using a TIG process. There is no addition of any material so the focus of modelling the process could be concentrated on the thermal analysis and the phase transformations. Temperature dependent material properties and a continuous cooling transformation (CCT) diagram of the base material were provided. The simulations took into account metallurgical effects and used a Goldak-type heat source. Simulations with and without phase transformations were carried out, in order to analyse the effect on the predicted residual stress.