J. J. Rhiu's research while affiliated with University of Maryland, College Park and other places

Publications (11)

Article
A 32-node three-dimensional solid element and a 16-node degenerate solid element that are applicable to analysis of thin-shell structural problems are presented in this paper. Both elements are formulated by using the Hellinger-Reissner principle with independent strain. The assumed independent strain field is divided into higher-and lower-order po...
Conference Paper
A mixed finite element formulation with stabilization matrix is presented for geometrically nonlinear thin shells. This formulation is based on the degenerate solid shell element concept and the Hellinger-Reissner principle with independent strain field. The independent strain field is divided into a lower order part and a higher order part. Using...
Article
A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger-Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic...
Article
A sixteen node shell element is developed using a matrix stabilization scheme based on the Hellinger-Reissner principle with independent strain. Initially the assumed independent strain is divided into a lower order part and a higher order part. The stiffness matrix corresponding to the lower order assumed strain is equivalent to the stiffness matr...
Chapter
A nine node finite element is developed for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger—Reissner principle with independent strain. Two versions of assumed independent strain are selected to suppress spurious kinematic m...
Article
A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger–Reissner principle with independent strain and the concept of a degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by div...
Article
A new mixed finite element formulation is developed based on the Hellinger-Reissner principle with independent strain. By dividing the assumed strain into its lower order and higher order parts, the new formulation can be made much more efficient than the conventional mixed formulation. In addition the present new approach provides an alternative w...
Article
A nine-node element, designated as SHEL9, has been developed for analysis of thin plates and shells. The element formulation is based on the degenerate solid shell concept and a modified Hellinger-Reissner principle with independent in-plane and transverse shear strains. Numerical tests indicate that the present SHEL9 element with uniform 3 × 3 poi...
Article
The analytical study of the nature of interlaminar stresses near stress free edges has been the subject of substantial research interest. Such studies are significant because the high interlaminar stresses or stress singularities near stress-free edges may cause delamination failure as shown by experimental investigations. Also the accurate predict...

Citations

... The idea for a satisfactory way of extending AMF to higher order element came from Rhiu & Lee's approach for improving the computational efficiency of hybrid strain element [48,49]. The approach has been employed to design higher order elements for plate/shell analysis [48,50,51] and is based on the strain-version of the Hellinger-Reissner functional : ...
... They have been the subjects of research for several decades. In this light, advanced formulations including but not limited to hybrid/mixed formulation [13][14][15][16][17][18][19][20], SRI (selectively reduced integration) [21,22], stabilization [14][15][16][17][18][23][24][25][26][27][28][29], incompatible displacement or enhanced assumed strain (EAS) method [30][31][32][33][34] have been proposed. However, advanced high order elements are rarely seen, probably because they are seldom used in stress analysis and advanced formulations also become more expensive in high order elements. ...
... The next step is to identify and suppress the zero-energy modes. The numerical approach to identify these modes is inspired from the work of Lee at el. [23,24]. Let be the strain energy of an element domain, which is defined by the following expression: The above expression leads to zero-strain energy if the admissible deformation ( ) coincides with the null space of . ...
... Three different thickness values are considered, that is, h = 3.175, 6.35, and 12.7 mm. The problem has been considered in Sabir and Lock, 40 Horrigmoe and Bergan, 41 Rhiu and Lee, 42 Sze et al., 32 and Arciniega and Reddy. 33 The arc-length control method is used to trace the equilibrium path, and a tolerance coefficient of 1:0 3 10 À6 is used. ...
... The next step is to identify and suppress the zero-energy modes. The numerical approach to identify these modes is inspired from the work of Lee at el. [23,24]. Let be the strain energy of an element domain, which is defined by the following expression: The above expression leads to zero-strain energy if the admissible deformation ( ) coincides with the null space of . ...
... Unfortunately, the so-formed elements encounter the risk of shear and membrane lockings as their thickness becomes small. To alleviate lockings, a number of noteworthy techniques have been proposed including uniformly reduced integration, selectively reduced integration (Zienkiewicz, Taylor & Too 1971;Hughes, Cohen & Haroun 1978), heterosis elements , c-stabilization method (Belytschko, Ong, Liu & Kennedy 1984;Belytschko, Wong & Stolarski 1989), hybrid/mixed formulation (Lee & Pian 1978;Lee, Dai, & Yeom 1985;Rhiu & Lee 1987;Rhiu & Lee 1988;Rhiu, Russel & Lee 1990;Saleeb, Chang, Graf & Yingyeunyong 1990;Kim & Lee 1992;Basar, Ding & Kraetzig 1992;Sze 1994b;Guan & Tang 1995;Sze, Yi & Tay 1997), assumed strain methods (MacNeal 1978;Bathe & Dvorkin 1986;Huang & Hinton 1986;Park & Stanley 1986;Belytschko, Wong & Stolarski 1989, Flores, Onate & Zarate 1995, etc. Among them, the URI (uniformly reduced integrated) elements have an outstanding accuracy and computational ef®ciency. ...