## 1 Introduction  
The finite element method (FEM) is one of the most successful numerical methods and has been widely used to solve mechanics problems in various engineering fields [1, 2, 3, 4, 5]. Despite its great success, the standard finite element method has some limitations: the analysis accuracy depends on the mesh used and the stress prediction accuracy is considerably poor when 3-node triangular (2D) and 4-node tetrahedral (3D) elements are used [6, 7, 5]. Many studies have been conducted to overcome these limitations of the standard FEM (ST-FEM), and several numerical methods, such as extended FEM (EX-FEM), enriched FEM (EN-FEM), and smoothed FEM (S-FEM), have been developed [8, 9, 10, 11, 12]. The S-FEM is a relatively recently proposed method among the several techniques mentioned above and has been successfully applied to various engineering problem [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. In S-FEM, the strain smoothing technique originally developed for the Galerkin mesh-free method is applied to the FEM, and constant strain fields are constructed in newly defined smoothing domains [13, 14]. Depending on how the smoothing domain is defined, node-based, cell-based, edge-based, and face-based smoothed FEM have been proposed. Each S-FEM has different characteristics and performance depending on the smoothing domain, and it is generally known that edge-based S-FEM (ES-FEM) is the most effective [20, 21, 22, 23]. The solution accuracy of the ES-FEM is more accurate compared to the ST-FEM, especially when the same lower order element mesh is used, and unlike other methods such as EX-FEM and EN-FEM, no additional degrees of freedoms (DOFs) are required [6, 8, 11, 25]. However, when high gradient occurs in the smoothing domain, the predictive ability of the ES-FEM with a lower order element mesh is not good enough to be used in engineering practice [25, 26]. The enrichment scheme was developed as another method of improving finite element solution accuracy [5; 9; 11]. With the enrichment scheme, the solution space of the standard finite element can be expanded by introducing cover functions corresponding to enriched DOFs. The main advantage of the enriched FEM (EN-FEM) is that the solution improvement in the sense of the p-version of the ST-FEM is available without introducing additional nodes. In addition, adaptively applying the cover function to a local area where solution accuracy needs to be improved can enhance solution accuracy efficiently [5; 11]. However, depending on the mesh used when applying the polynomial cover function, a linear dependence (LD) problem that leads to ill-conditioned global matrices can occur [27; 28]. Many methods have been suggested to suppress the LD problem of enriched finite elements [3; 29; 30; 31]. Among the suggested methods, the LD problem was resolved in a simple and effective way by adopting piecewise linear shape functions and suppressing enriched DOFs [32; 33]. In addition, a procedure for automatically improving the analysis accuracy of the standard finite elements using enriched finite elements has been proposed [34; 35]. In this procedure, the use of cover functions is determined automatically based on the analysis results of the standard finite elements. The mesh-refinement is not required, but the number of DOFs used increases. In this paper, we propose an automatic procedure to effectively improve the solution accuracy of edge-based 2D solid finite elements (4-node quadrilateral and 3-node triangular) without mesh-refinement or introducing additional nodes. An error indicator that estimates the error of the finite element solution and cover function selection scheme based on the error indicator are adopted, and the enriched finite elements are employed to incorporate cover functions in the analysis results. The adaptive enrichment scheme can enhance the solution of edge-based finite elements and capture high gradients efficiently.