The high-order completeness analysis of the scaled boundary finite element method

Three‐dimensional spline scaled boundary finite elements with high‐order completeness

“…Proof From the interpolation property of the quadratic quadrilateral element, the Serendipity element Q8 only has linear completeness, while the Lagrange element Q9 and the spline element L8 have the second‐order completeness 31,32 . Therefore, by the completeness theorem in Reference 29, the completeness of 3D scaled boundary finite elements is decided by that of the surface elements they adopt. Thus, SBFEM‐Q8 has linear completeness, while SBFEM‐Q9 and SBFEM‐L8 have the second‐order completeness.…”

“…Reference 28 presents the development of novel high‐order complete shape functions over star‐convex polygons by including bubble functions derived from the body force modes based on the SBFEM. Reference 29 analyzes the high‐order completeness of the SBFEM in mathematics for two‐dimensional and 3D problems. Due to the semi‐analytic properties, the completeness of conforming elements is guaranteed by the accuracy of line elements or surface elements in the SBFEM.…”

Linear interface crack under harmonic shear: Effects of crack's faces closure and friction

“…A semianalytical approach, namely the scaled boundary finite element method, was used to model crack face contact and propagation problems in [18][19][20]. The high-order completeness analysis of the method was provided in [21].…”

A polygonal element for couple stress/strain gradient elasticity based on SBFEM and spline interpolation

“…而且, 由于SBFEM特殊的单元构造方法, 只要求"比例中 心"与边界节点的连线位于单元内部即可, 因此非凸 或退化的多边形单元的计算与凸多边形单元一致, 单元之间的协调性不会受到悬节点的影响, 并能获 得很好的计算精度 [35] . 最近, 在文献 [36] [11,13]…”

“…分别计算的单元应变梯度刚度矩阵( 52)或(54), 相加 即可得到基于多边形的应变梯度理论单元刚度矩 阵( 19)或者偶应力理论的单元刚度矩阵 (20). 结合 文献 [36,37]的理论结果, 可知组合单元SBFEMd3-DKPS2对偶应力和应变梯度理论都能精确重构满 足体力为零的平衡方程的任意2次多项式位移函数.…”