Nonlinear Finite-Element Method for Plates and Its Application to Dynamic Response of Reactor Fuel Subassemblies

1974 ◽  
Vol 96 (4) ◽  
pp. 251-257 ◽  
Author(s):  
T. Belytschko ◽  
A. H. Marchertas
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shell Element ◽  
Nonlinear Material ◽  
Time Step ◽  
Cross Sectional ◽  
Difference Formula ◽  
Lumped Masses

A finite-element procedure for transient analysis of plates and shells in three-dimensional space, and applicable to large displacements and nonlinear material properties, is described. This procedure employs a convected coordinate formulation enabling the use of simple strain-nodal displacement and nodal force-stress relations. The plate/shell element considers linear in-plane displacements and cubic transverse displacements. The orientation of lumped masses is described by unit vectors so that arbitrarily large rotations can be treated. Discretized equations of motion are integrated explicitly in time with a difference formula. Membrane artificial viscosity is utilized to stabilize occasional oscillations. The computational efficiency of the procedure is quite good: one element-time step takes 2 msec on an IBM 360/195 computer. Comparison of results with experimental data of impulsively loaded plates shows good agreement. The program was applied to a hexagonal fuel subassembly loaded internally. Various results are presented on its response and it is shown that, for that type of loading, two-dimensional cross-sectional models may be adequate.

scholarly journals A Finite Element Formulation for Fluid-Structure Interaction in Three-Dimensional Space

1981 ◽  
Vol 103 (2) ◽  
pp. 183-190 ◽  
Author(s):  
R. F. Kulak
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Three Dimensional ◽  
Element Formulation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Discrete Equations ◽  
Numerical Predictions

In this paper a development is presented for a three-dimensional hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using an explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading.

A Finite Element Formulation for the Dynamic Analysis of Machine Components Fabricated From Composite Materials

1992 ◽  
Author(s):  
A. Semos ◽  
C. Chassapis
Keyword(s):  
Finite Element ◽  
Composite Materials ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Element Formulation ◽  
Reinforced Composite ◽  
External Forces ◽  
Three Dimensional Space

Abstract In this paper finite element procedures are presented for analyzing the elastic-dynamic behavior of mechanical components fabricated from fiber-reinforced composite materials. An arbitrarily laminated composite plate element is created which allows the analysis of components that are moving in three dimensional space. The five D.O.F. per node static model of S. C. Panda and R. Natarajan is used as a basis for the derivation of the dynamic model. The elemental equations of motion are derived from Hamilton’s Principle. The formulation considers the total kinetic and strain energies of the moving element, together with the work due to bending, caused by the transversely acting external forces, as well as that due to the foreshortening of the element, caused by axially applied loads.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

Large- and small-scale vortical motions in a shear layer perturbed by tabs

1999 ◽  
Vol 382 ◽  
pp. 307-329 ◽  
Author(s):  
JUDITH K. FOSS ◽  
K. B. M. Q. ZAMAN
Keyword(s):  
Shear Layer ◽  
Pitch Angle ◽  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Scale Population

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

A Finite Element for the Analysis of Shell Intersections

1996 ◽  
Vol 118 (4) ◽  
pp. 399-406 ◽  
Author(s):  
W. J. Koves ◽  
S. Nair
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Three Dimensional ◽  
Shell Element ◽  
Theory Of Elasticity ◽  
Shell Elements ◽  
Asme Code ◽  
Form Theory ◽  
Computation Scheme ◽  
Shell Intersections

A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed and has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections (Koves, 1993). The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems.

Shape Opimization of Femoral Components of an Artificial Hip Prosthesis Using the Three-Dimensional P-Version Finite Element Method

2001 ◽  
Author(s):  
Masaru Higa ◽  
Ikuya Nishimura ◽  
Hiromasa Tanino ◽  
Yoshinori Mitamura
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hip Prosthesis ◽  
Three Dimensional ◽  
Optimization Procedure ◽  
Peak Stress ◽  
Cross Sectional ◽  
Design Variables ◽  
Dimensional Shape ◽  
Element Method

Abstract The three-dimensional shape optimization of cemented total hip arthroplasty (THA) was introduced in this paper. The P-version Finite Element Method (FEM) combined with an optimization procedure was used to minimize the peak stress in the bone cement near the tip of the implant. Six-design variables were used in this study. Each variable represents the dimension of the medial-lateral width and anterior-posterior width of the three levels (proximal, distal and middle) of cross sectional area of the prosthesis. The results of the design optimization showed considerable reduction in stress concentration compared to the initial design that is currently used clinically.

scholarly journals Domain Decomposition Modified with Characteristic Mixed Finite Element and Numerical Analysis for Three-Dimensional Slightly Compressible Oil-Water Seepage Displacement

2017 ◽  
Vol 9 (1) ◽  
pp. 143
Author(s):  
Yirang Yuan ◽  
Luo Chang ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Method Of Characteristics ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Optimal Error Estimate ◽  
Computational Domain ◽  
Time Step ◽  
Slightly Compressible ◽  
The Method Of Characteristics

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in $l^2$ norm. Numerical example is given to testify theoretical analysis and numerical data show that this method is effective in solving actual applications. Then it can solve the well-known problem.

Dual Representation Methods for Efficient and Automatable Analysis of 3D Plates

2010 ◽  
Vol 10 (4) ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Computer Aided Design ◽  
Dimensional Space ◽  
Reduction Process ◽  
Thin Plates ◽  
Design Environment ◽  
Element Analysis ◽  
Cross Sectional ◽  
Dual Representation ◽  
3D Finite Element

It is well recognized that 3D finite element analysis is inappropriate for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2D methods have been developed for analyzing such structures. However, 2D methods pose serious automation challenges in today’s 3D design environment. Specifically, analysts must manually extract cross-sectional properties from a 3D computer aided design (CAD) model and import them into a 2D environment for analysis. In this paper, we propose two efficient yet easily automatable dual representation methods for analyzing thin plates. The first method exploits standard off-the-shelf 3D finite element packages and achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3D plate bending stiffness matrix is constructed from a 3D mesh and then projected onto a lower-dimensional space by appealing to standard 2D plate theories. In the second method, the analysis is carried out by integrating 2D shape functions over the boundary of the 3D plate. Both methods do not entail extraction of the cross-sectional properties of the plate. However, the user must identify the plate or thickness direction. The proposed methodologies are substantiated through numerical experiments.

Sign in / Sign up

Export Citation Format

Share Document