This paper presents automated meshing and unit cell analysis techniques for periodic composites using hierarchical tri-quadratic tetrahedral elements. The method starts with a hierarchical quad-tree (2D) or octree (3D) mesh of pixel or voxel elements, then applies successive element splitting and nodal shifting to generate final meshes that accurately capture material arrangements and constituent volume fractions. The techniques are demonstrated on densely packed fibre and particulate composites, and 3D textile-reinforced composites. The proposed methods address two key challenges in finite element-based computational homogenization: high computational cost and the difficulty of creating suitable material-scale finite element models. The methods use material domain identification functions (MDIFs) to identify material regions and ensure accurate meshing. The techniques involve creating a hierarchical pixel/voxel mesh, splitting into triangles or tetrahedra, and then applying nodal shifting and element splitting to achieve homogeneous meshes. The methods also address the issue of periodic boundary conditions and ensure compatibility between adjacent unit cells. The proposed techniques are validated through numerical examples showing convergence of effective properties of composites. The methods are particularly effective for composites with complex material arrangements, as they allow for accurate representation of material interfaces and volume fractions. The techniques are implemented using a combination of hierarchical meshing and nodal shifting, and are applicable to both 2D and 3D composites. The results demonstrate the effectiveness of the proposed methods in accurately capturing material interfaces and computing effective properties of composites.This paper presents automated meshing and unit cell analysis techniques for periodic composites using hierarchical tri-quadratic tetrahedral elements. The method starts with a hierarchical quad-tree (2D) or octree (3D) mesh of pixel or voxel elements, then applies successive element splitting and nodal shifting to generate final meshes that accurately capture material arrangements and constituent volume fractions. The techniques are demonstrated on densely packed fibre and particulate composites, and 3D textile-reinforced composites. The proposed methods address two key challenges in finite element-based computational homogenization: high computational cost and the difficulty of creating suitable material-scale finite element models. The methods use material domain identification functions (MDIFs) to identify material regions and ensure accurate meshing. The techniques involve creating a hierarchical pixel/voxel mesh, splitting into triangles or tetrahedra, and then applying nodal shifting and element splitting to achieve homogeneous meshes. The methods also address the issue of periodic boundary conditions and ensure compatibility between adjacent unit cells. The proposed techniques are validated through numerical examples showing convergence of effective properties of composites. The methods are particularly effective for composites with complex material arrangements, as they allow for accurate representation of material interfaces and volume fractions. The techniques are implemented using a combination of hierarchical meshing and nodal shifting, and are applicable to both 2D and 3D composites. The results demonstrate the effectiveness of the proposed methods in accurately capturing material interfaces and computing effective properties of composites.