Several New Low-Order Elements In FEM And A Systematic Method To Construct Residual Stresses Induced By Welding

After recalling the development and application of low-order elements with high performance, the methods applied to determine residual stresses caused by welding and the typical work of inverse elastic problems, the following work, which is related to the development of new low-order elements with high performance and the method for the construction of residual stresses induced by welding, has been carried out in this paper:1. A new strategy has been suggested to improve the performance of the EAS elements. In order to achieve high accuracy with EAS element under irregular mesh, a new strategy to improve the EAS element proposed by has been suggested. Based on the strategy, two kinds of new elements have been presented, the numerical examples show that the new elements can produce better results than the original one.2. A 3D penalty equilibrating hybrid element based on Hu-Washizu variational principle has been proposed. Based on the Hu-Washizu variational principle, a 3D penalty equilibrating hybrid element has been proposed, which is suitable for the material nonlinear analysis, e.g. elastic-plastic analysis. The numerical examples show that the new element can also be used to analyze plate and shell problems.3. The 3D penalty equilibrating hybrid element has been extended to elastic-plastic analysis. The formulations of the 3D penalty equilibrating hybrid element for elastic-plastic analysis, together with the sequence of calculations performed in iteration, have been presented.4. A new strategy of the selection of the penalty factor in 3D penalty equilibrating hybrid element has been presented. Taking the "trapezoid-locking" problems as an example, the reason for the better results of the penalty technique has been investigated. The relation between the penalty factor in the plane penalty equilibrating hybrid stress element and the selective-reduced factor used in the PS element has been further discussed. Bearing the discussion in mind, a new strategy of the selection of the penalty factor in 3D penalty equilibrating hybrid element has been presented to improve the performance of the element when applied to beam, plate andshell problems. Some numerical examples have demonstrated the effectiveness of the new strategy.5. A strategy to construct the residual stresses induced by welding has been proposed. Residual stresses are inevitably produced during the procedure of welding because of the high thermal gradient. The residual stresses can greatly affect the performance of structures, such as fatigue life and compression strength etc. Therefore in the second part of this paper, a systematic strategy has been established which can be applied to construct the residual stresses which meet the self-equilibrium condition and boundary condition with less experimental information compared with the inherent strain method. Moreover, with the help of the user interface, the identified results can be conveniently planted into the commercial FEM software, e.g. ABAQUS, then the influence of the residual stresses on the performance of the structures can be evaluated instantly, e.g. the evaluation of the effect of residual stresses on crack growth and stability. Considering the efficiency and accuracy in finite element analysis in the present method, a B-bar element proposed by Piltner and Taylor has been used, in this paper, the analytical integration of the stiffness matrix obtained using the software Maple V is applied to replace the traditional numerical integral strategy and the efficiency of the refined element is as high as the displacement-based element.