## 3 Non-Penalisation Smooth-Edged Material Distribution for Optimising Topology  
The Smooth-Edged Material Distribution for Optimising Topology (SEMDOT) method proposed by [PERSON] et al. [12] is a newly developed optimisation tool that is capable of forming smooth topological boundaries without needing any post-processing treatments, such as shape optimisation, before fabrication. This improves the manufacturability of the obtained topologies; hence, SEMDOT is widely used in Design for Additive Manufacturing (DfAM) [55; 56; 57]. Most recently, [PERSON] et al. [13] improved SEMDOT by removing the material penalisation scheme. Compared to penalised SEMDOT, the structural performance and the convergency of non-penalised SEMDOT are significantly improved. Although the effectiveness of non-penalised SEMDOT is validated by representative benchmark problems [13], non-penalised SEMDOT has not been used to solve real-world optimisation problems yet. This work aims to adopt non-penalised SEMDOT to conduct the optimisation of the Sheikh-Ibrahim's connection tension cover plate. SEMDOT forms a smooth topological boundary based on the solid/void design of the grid points that are independently assigned to each element [12; 13]. In SEMDOT, the Young's modulus of a grid point is calculated by:  
\[E_{\epsilon}\big{(}\rho_{\epsilon,g}\big{)}=\rho_{\epsilon,g}E^{1} \tag{1}\]  
where \(\rho_{\epsilon,g}\) is the scaling value of the gth grid point assigned to the \(e\)th element, which is named the grid point density; \(E_{\epsilon}(\rho_{\epsilon,g})\) is the function of the Young's modulus with respect to grid point densities; and \(E^{1}\) is the Young's modulus of the solid material. To conduct finite element analysis in SEMDOT, elemental volume fractions that depend on grid point densities are defined as surrogate design variables, which have the form:  
\[X_{\epsilon}=\frac{1}{N}\sum_{g=1}^{N}\rho_{\epsilon,g} \tag{2}\]  
where \(X_{\epsilon}\) is the volume fraction of the \(e\)th element and \(N\) is the total number of grid points in each element. Based on Equations (1) and (2), the stiffness matrix of a solid or void element is:  
\[\mathbf{K}_{e}(X_{\epsilon})=X_{\epsilon}\mathbf{K}_{e}^{1} \tag{3}\]  
where \(\mathbf{K}_{e}^{1}\) is the stiffness matrix of the solid element. In SEMDOT, the boundary elements are artificially defined as the non-homogenised combination of solid and void materials, and therefore elemental stiffness matrices are estimated using a linear interpolation between the two phases of solid and void:  
\[\mathbf{K}_{e}(X_{\epsilon})=(1-X_{\epsilon})\mathbf{K}_{e}^{0}+X_{\epsilon} \mathbf{K}_{e}^{1} \tag{4}\]  
where \(\mathbf{K}_{e}^{0}\) is the stiffness matrix of the void element. To avoid mesh dependency and checkerboard patterns, the filtering for elemental volume fractions \(X_{\epsilon}\) is  
\[\widetilde{X}_{\epsilon}=\frac{\sum_{l=1}^{N_{\epsilon}}\omega_{el}X_{l}}{ \sum_{l=1}^{N_{\epsilon}}\omega_{el}} \tag{5}\]  
where \(\widetilde{X}_{\epsilon}\) is the filtered elemental volume fraction; \(N_{\epsilon}\) is the neighborhood set of elements within the filter domain for the \(e\)th element, which is a circle at the center of this element with a given filter radius \(r_{\text{min}}\); and \(\omega_{el}\) is a weight factor, which is calculated by  
\[\omega_{el}=\max(0,r_{\text{min}}-\Delta(e,l)) \tag{6}\]  
where \(\Delta(e,l)\) is the center-to-center distance of the \(l\)th element within the filter domain to the \(e\)th element. Nodal densities are obtained by:  
\[\rho_{n}=\frac{\sum_{e=1}^{M}\omega_{ne}\widetilde{X}_{e}}{\sum_{e=1}^{M}\omega_{ ne}} \tag{7}\]  
where \(\rho_{n}\) is the density of the \(n\)th node, \(M\) is the total number of elements, and \(\omega_{ne}\) is the weight factor defined as  
\[\omega_{ne}=\max(0,R_{\min}-\Delta(n,e)) \tag{8}\]  
where \(\Delta(n,e)\) is the distance between the \(n\)th node and the center of the \(e\)th element and \(R_{\min}\) is the filter radius. In SEMDOT, \(R_{\min}\) is generally set to 1.