• Structural Engineering and Mechanics
• /
• v.63 no.2
• /
• pp.225-235
• /
• 2017

In this paper a vibration study on orthotropic elliptic paraboloid shells with openings is carried out by using a hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Natural frequencies of orthotropic elliptic paraboloid shells with and without openings are presented. The influence of aspect ratio, height ratio, opening ratio and material angle on the frequencies and mode shapes are investigated.

• Structural Engineering and Mechanics
• /
• v.37 no.6
• /
• pp.633-648
• /
• 2011

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., $\mathbf{B}$-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.

• Steel and Composite Structures
• /
• v.11 no.5
• /
• pp.359-374
• /
• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• Structural Engineering and Mechanics
• /
• v.62 no.1
• /
• pp.11-20
• /
• 2017

The base force element method (BFEM) is a new finite element method. In this paper, a degenerated 4-mid-node plane element from concave polygonal element of BFEM was proposed. The performance of this quadrilateral element with 4 mid-edge nodes in the BFEM on complementary energy principle is studied. Four examples of linear elastic analysis for plane frame structure are presented. The influence of aspect ratio of the element is analyzed. The feasibility of the 4 mid-edge node element model of BFEM on complementary energy principles researched for plane frame problems. The results using the BFEM are compared with corresponding analytical solutions and those obtained from the standard displacement finite element method. It is revealed that the BFEM has better performance compared to the displacement model in the case of large aspect ratio.

• Structural Engineering and Mechanics
• /
• v.27 no.3
• /
• pp.311-331
• /
• 2007

The purpose of this paper is to study shear locking-free analysis of thick plates using Mindlin's theory and to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick plates subjected to uniformly distributed loads. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 8- and 17-noded quadrilateral finite elements are used. Graphs and tables are presented that should help engineers in the design of thick plates. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates. It is also concluded, in general, that the maximum displacement and bending moment increase with increasing aspect ratio, and that the results obtained in this study are better than the results given in the literature.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2003.05a
• /
• pp.258-261
• /
• 2003

In this study, finite element analysis for multi-stage deep drawing process of rectangular configuration with extreme aspect ratio is carried out especially for the blank design. The analysis of rectangular deep drawing process with extreme aspect ratio is likewise very difficult with respect to the design process parameters including the intermediate die profile. In order to solve the difficulties, numerical approach using finite element method is performed in the present analysis and design. A series of experiments for multi-stage rectangular deep drawing process are conducted and the deformed configuration is investigated by comparing with the results of the finite element analysis. Additionally, to minimize amount of removal material after trimming process, finite element simulation is applied for the blank modification. The analysis incorporates brick elements for a rigid-plastic finite element method with an explicit time integration scheme using LS-DYNA3D.

• Structural Engineering and Mechanics
• /
• v.33 no.3
• /
• pp.373-385
• /
• 2009

The purpose of this paper is to study shear locking-free parametric earthquake analysis of thick and thin plates using Mindlin's theory, to determine the effects of the thickness/span ratio, the aspect ratio and the boundary conditions on the linear responses of thick and thin plates subjected to earthquake excitations. In the analysis, finite element method is used for spatial integration and the Newmark-${\beta}$ method is used for the time integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the earthquake analysis of thick and thin plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Journal of Korean Association for Spatial Structures
• /
• v.3 no.2 s.8
• /
• pp.85-90
• /
• 2003

If we use a third order approximation for the displacement function of beam element in finite element methods, finite element solutions of beams yield nodal displacement values matching to beam theory results to have no connection with the number increasing of elements of beams. It is assumed that, as the member displacement value at beam nodes are correct, the calculation procedure of beam element stiffness matrix have no numerical errors. A the member forces are calculated by the equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$, the member forces at nodes of beams have errors in a moment and a shear magnitudes in the case of smaller number of element. The nodal displacement value of plate subject to the lateral load converge to the exact values according to the increase of the number of the element. So it is assumed that the procedures of plate element stiffness matrix calculations has a error in the fundamental assumptions. The beam methods for the high accuracy ratio solution Is also applied to the plate analysis. The method of reducing a error ratio of member forces and element stiffness matrix in the finite element methods is studied. Results of study were as follows. 1. The matrixes of EI[B] and [K] in the equations of M(x)=EI[B]{q} and M(x) = [K]{q}+{Q} of beams are same. 2. The equations of $\frac{-M}{EI}=\frac{{d^2}{\omega}}{dx^2}\;and\;\frac{dM}{dx}=V$ for the member forces have a error ratio in a finite element method of uniformly loaded structures, so equilibrium node loads {Q} must be substituted in the equation of member forces as the numerical examples of this paper revealed.

• Steel and Composite Structures
• /
• v.23 no.6
• /
• pp.737-746
• /
• 2017

In this paper the influence of aspect ratio, height ratio and material angle on static and free vibration behaviour of orthotropic elliptic paraboloid shells is studied by using a four-node hybrid stress finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. A parametric study is carried out for static and free vibration response of orthotropic elliptic paraboloid shells with respect to displacements, internal forces, fundamental frequencies and mode shapes by varying the aspect and height ratios, and material angle.

• Structural Engineering and Mechanics
• /
• v.65 no.3
• /
• pp.213-222
• /
• 2018

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.