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In the finite element method, the conventional linear elements have long been precluded, due to their low accuracy of nodal displacements, from the analysis of super-convergence and adaptivity via the element energy projection (EEP) technique. To overcome this problem, in this paper, a nodal accuracy improvement technique is proposed for linear elements in 1D to 3D problems. In this method, a residual nodal load vector is derived with the conventional EEP solution, and a simple back-substitution process can generate the improved nodal displacements without changing the global stiffness matrix. Subsequently, an improved EEP scheme for linear elements is proposed based on the improved nodal displacements. Finally, by using the improved EEP solution as an error estimator, a two-phased adaptive algorithm is presented. Numerical examples show that the accuracy of nodal displacements is improved from the second-order convergence to the fourth-order convergence by using the nodal accuracy improvement technique, and the EEP solutions for element interior displacements are improved from the second-order convergence to the third-order convergence by using the improved EEP scheme. Therefore, the improved EEP scheme can be effectively used as an error estimator in adaptivity analysis for linear elements, which turns out to be efficient in general and even outperforms cubic elements for singularity problems. Full article

The finite element (FE) method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D) modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM) for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D) mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP) method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages. Full article