Comparative study of thermal post-buckling analysis of uniform slender & shear flexible columns using rigorous finite element and intuitive formulations

Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged-hinged, clamped-clamped and clamped-hinged conditions and nonclassical boundary conditions like the hinged-guided or the clamped-guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns.     

Numerical analysis of projection welding on auto-body sheet metal using a coupled finite element method

A comprehensive finite element method employing a subroutine to link up submodules of commercial code ANSYS is proposed to perform analysis of projection welding in quantitative detail. In order to solve the complexity due to dynamic changes in heat and electrical current flow paths, as well as temperature-dependent material properties, information about contact interfaces and the geometry of the projection areas have been taken into account. By updating parameter information among these submodules in an incremental manner, a truly thermal-electrical-mechanical coupled numerical analysis is realized for projection welding simulation. A case study of an automotive door assembly welding process is carried out and a series of experiments is conducted to confirm the validity of the newly developed method. The agreement between the experimental and numerical results is satisfactory, indicating that the incrementally coupled finite element method may be suitable for projection welding research. Finally, future work to extend this method in optimizing projection welding process design is also presented.     

Method for determination of the displacement field in patterned nanostructures by TEM/CBED analysis of split high-order Laue zone line profiles

A method to extract accurate information on the displacement field distribution from split high‐order Laue zones lines in a convergent‐beam electron diffraction pattern of nanostructures has been developed. Starting from two‐dimensional many beam dynamical simulation of HOLZ patterns, we assembled a recursive procedure to reconstruct the displacement field in the investigated regions of the sample, based on the best fit of a parametrized model. This recursive procedure minimizes the differences between simulated and experimental patterns, taken in strained regions, by comparing the corresponding rocking curves of a number of high‐order Laue zone reflections. Due to its sensitivity to small displacement variations along the electron beam direction, this method is able to discriminate between different models, and can be also used to map a strain field component in the specimen. We tested this method in a series of experimental convergent‐beam electron diffraction patterns, taken in a shallow trench isolation structure. The method presented here is of general validity and, in principle, it can be applied to any sample where not negligible strain gradients along the beam direction are present.