H- Versus P-Version FEM for Shell Analysis

1995 ◽  
Author(s):  
Jacob Fish ◽  
Ravi Guttal
Keyword(s):  
Computational Efficiency ◽  
Numerical Experiments ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Shell Elements ◽  
Quadrature Scheme ◽  
Assumed Strain ◽  
Shell Analysis ◽  
Speed Up

Abstract Research efforts aimed at optimizing the computational efficiency of the p-method are described. These include (i) a novel quadrature scheme for hierarchical shell elements, (ii) a family of assumed strain hierarchical shell elements, (iii) selective polynomial order escalation for assumed strain elements, and (iv) accelerated multi-grid-like solution procedures. Numerical experiments indicate that with these enhancements it is possible to speed up the overall computational time of p-method for analysis of shells by a factor greater than three for relatively small problems (less than 10,000 degrees of freedom), while computational savings for larger problems are even more significant. It has been found that the performance of the enhanced variant of the p-method for shells is comparable to that of the h-method for low accuracy requirements, and better if higher accuracies are desired.

scholarly journals EAS 3D triangular and quadrangular shell elements

2010 ◽  
pp. 205-215
Author(s):  
Philippe Jetteur ◽  
Philippe Pasquet
Keyword(s):  
Degrees Of Freedom ◽  
Shell Element ◽  
Element Formulation ◽  
Shell Elements ◽  
Assumed Strain ◽  
Definition Of ◽  
3D Solid ◽  
Assumed Strain Method ◽  
Internal Degrees Of Freedom

A new 3D solid shell element is developed in SAMCEF™ code. The purpose of this element is to make the meshing easier starting from a 3D definition of the structure, it is not necessary to extract the mean surface of the shell. Here, we are not concerned by the meshing; we only are concerned by the element formulation. In order to improve the quality of the results, we add internal degrees of freedom as suggested by Simo and co-authors. We use the Enhanced Assumed Strain method. A special handling of the transverse shear is performed in order to pass successfully the plate patch test (constant bending) and to avoid shear locking. The formulation is based on the work of Bathe and Dvorkin for classical shell. The element has been developed in linear and non-linear analysis; it can be a mono or multilayer element.

scholarly journals Generalised assumed strain curved shell finite elements (CSFE-sh) with shifted-Lagrange and applications on N-T’s shells theory

2020 ◽  
Vol 7 (1) ◽  
pp. 125-138
Author(s):  
Joseph Nkongho Anyi ◽  
Jean Chills Amba ◽  
Dieudonné Essola ◽  
Ngayihi Abbe Claude Valery ◽  
Merlin Bodol Momha ◽  
...  
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Benchmark Problems ◽  
Engineering Practice ◽  
Concentrated Load ◽  
Shell Elements ◽  
Assumed Strain ◽  
Rigid Body Modes ◽  
Shell Equations ◽  
Three Degrees Of Freedom

AbstractWe present a simple methodology to design curved shell finite elements based on Nzengwa-Tagne’s shell equations. The element has three degrees of freedom at each node. The displacements field of the element satisfies the exact requirement of rigid body modes in a ‘shifted-Lagrange’ polynomial basis. The element is based on independent strain assumption insofar as it is allowed by the compatibility equations. The element developed herein is first validated on analysis of benchmark problems involving a standard shell with simply supported edges. Examples illustrating the accuracy improvement are included in the analysis. It showed that reasonably accurate results were obtained even when using fewer elements compared to other shell elements. The element is then used to analyse spherical roof structures. The distribution of the various components of deflection is obtained. Furthermore, the effect of introducing concentrated load on a cylindrical clamped ends structure is investigated. It is found that the CSFE3-sh element considered is a very good candidate for the analysis of general shell structures in engineering practice in which the ratio h/R ranges between 1/1000 and 2/5.

scholarly journals An Algorithm Based on Loop Cutting Contribution Function for Loop Cutset Problem in Bayesian Network

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 462
Author(s):  
Jie Wei ◽  
Yufeng Nie ◽  
Wenxian Xie
Keyword(s):  
Bayesian Inference ◽  
Bayesian Network ◽  
Network Structure ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Global Perspective ◽  
Node Pair ◽  
Bayesian Network Structure ◽  
Network Structure Analysis ◽  
Contribution Index

The loop cutset solving algorithm in the Bayesian network is particularly important for Bayesian inference. This paper proposes an algorithm for solving the approximate minimum loop cutset based on the loop cutting contribution index. Compared with the existing algorithms, the algorithm uses the loop cutting contribution index of nodes and node-pairs to analyze nodes from a global perspective, and select loop cutset candidates with node-pair as the unit. The algorithm uses the parameter μ to control the range of node pairs, and the parameter ω to control the selection conditions of the node pairs, so that the algorithm can adjust the parameters according to the size of the Bayesian networks, which ensures computational efficiency. The numerical experiments show that the calculation efficiency of the algorithm is significantly improved when it is consistent with the accuracy of the existing algorithm; the experiments also studied the influence of parameter settings on calculation efficiency using trend analysis and two-way analysis of variance. The loop cutset solving algorithm based on the loop cutting contribution index uses the node-pair as the unit to solve the loop cutset, which helps to improve the efficiency of Bayesian inference and Bayesian network structure analysis.

scholarly journals Finite-Horizon Kinetic Energy Optimization of a Redundant Space Manipulator

2021 ◽  
Vol 11 (5) ◽  
pp. 2346
Author(s):  
Alessandro Tringali ◽  
Silvio Cocuzza
Keyword(s):  
Kinetic Energy ◽  
Real Time ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Computational Time ◽  
Redundant Manipulators ◽  
Space Robotics ◽  
Optimal Method ◽  
End Effector ◽  
Global Optimal

The minimization of energy consumption is of the utmost importance in space robotics. For redundant manipulators tracking a desired end-effector trajectory, most of the proposed solutions are based on locally optimal inverse kinematics methods. On the one hand, these methods are suitable for real-time implementation; nevertheless, on the other hand, they often provide solutions quite far from the globally optimal one and, moreover, are prone to singularities. In this paper, a novel inverse kinematics method for redundant manipulators is presented, which overcomes the above mentioned issues and is suitable for real-time implementation. The proposed method is based on the optimization of the kinetic energy integral on a limited subset of future end-effector path points, making the manipulator joints to move in the direction of minimum kinetic energy. The proposed method is tested by simulation of a three degrees of freedom (DOF) planar manipulator in a number of test cases, and its performance is compared to the classical pseudoinverse solution and to a global optimal method. The proposed method outperforms the pseudoinverse-based one and proves to be able to avoid singularities. Furthermore, it provides a solution very close to the global optimal one with a much lower computational time, which is compatible for real-time implementation.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Integrated Redesign of Large-Scale Structures by Large Admissible Perturbations

2003 ◽  
Vol 125 (4) ◽  
pp. 234-241 ◽  
Author(s):  
Vincent Y. Blouin ◽  
Michael M. Bernitsas ◽  
Denby Morrison
Keyword(s):  
Degrees Of Freedom ◽  
Large Scale ◽  
Direct Method ◽  
Computational Effort ◽  
Forced Response ◽  
Response Amplitude ◽  
Computational Time ◽  
Performance Constraints ◽  
Large Admissible Perturbations ◽  
Design Selection

In structural redesign (inverse design), selection of the number and type of performance constraints is a major challenge. This issue is directly related to the computational effort and, most importantly, to the success of the optimization solver in finding a solution. These issues are the focus of this paper, which provides and discusses techniques that can help designers formulate a well-posed integrated complex redesign problem. LargE Admissible Perturbations (LEAP) is a general methodology, which solves redesign problems of complex structures with, among others, free vibration, static deformation, and forced response amplitude constraints. The existing algorithm, referred to as the Incremental Method is improved in this paper for problems with static and forced response amplitude constraints. This new algorithm, referred to as the Direct Method, offers comparable level of accuracy for less computational time and provides robustness in solving large-scale redesign problems in the presence of damping, nonstructural mass, and fluid-structure interaction effects. Common redesign problems include several natural frequency constraints and forced response amplitude constraints at various frequencies of excitation. Several locations on the structure and degrees of freedom can be constrained simultaneously. The designer must exercise judgment and physical intuition to limit the number of constraints and consequently the computational time. Strategies and guidelines are discussed. Such techniques are presented and applied to a 2,694 degree of freedom offshore tower.

Introducing a Projection-Based Method to Compare Three Approaches Computing the Accumulation of Geometric Variations

2018 ◽  
Author(s):  
Vincent Delos ◽  
Santiago Arroyave-Tobón ◽  
Denis Teissandier
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Design ◽  
Geometric Constraints ◽  
Computational Time ◽  
Manufacturing Defects ◽  
Design Tolerance ◽  
Polyhedral Objects ◽  
The Difference ◽  
Bounded Sets ◽  
Accumulation Of Defects

In mechanical design, tolerance zones and contact gaps can be represented by sets of geometric constraints. For computing the accumulation of possible manufacturing defects, these sets have to be summed and/or intersected according to the assembly architecture. The advantage of this approach is its robustness for treating even over-constrained mechanisms i.e. mechanisms in which some degrees of freedom are suppressed in a redundant way. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In this work, we compare three methods for summing sets of constraints using polyhedral objects. The difference between them lie in the way the degrees of freedom (DOFs) (or invariance) of joints and features are treated. The first method proposes to virtually limit the DOFs of the toleranced features and joints to turn the polyhedra into polytopes and avoid manipulating unbounded objects. Even though this approach enables to sum, it also introduces bounding or cap facets which increase the complexity of the operand sets. This complexity increases after each operation until becoming far too significant. The second method aims to face this problem by cleaning, after each sum, the calculated polytope to keep under control the effects of the propagation of the DOFs. The third method is new and based on the identification of the sub-space in which the projection of the operands are bounded sets. Calculating the sum in this sub-space allows reducing significantly the operands complexity and consequently the computational time. After presenting the geometric properties on which the approaches rely, we demonstrate them on an industrial case. Then we compare the computation times and deduce the equality of the results of all the methods.

scholarly journals Smoothed Particle Hydrodynamics Simulation of a Mariculture Platform under Waves

Water ◽  
2021 ◽  
Vol 13 (20) ◽  
pp. 2847
Author(s):  
Feng Zhang ◽  
Li Zhang ◽  
Yanshuang Xie ◽  
Zhiyuan Wang ◽  
Shaoping Shang
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Graphics Processing Units ◽  
Degrees Of Freedom ◽  
High Tide ◽  
Theoretical Data ◽  
Emergency Evacuation ◽  
Water Levels ◽  
Computational Time ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

This work investigates the dynamic behaviors of floating structures with moorings using open−source software for smoothed particle hydrodynamics. DualSPHysics permits us to use graphics processing units to recreate designs that include complex calculations at high resolution with reasonable computational time. A free damped oscillation was simulated, and its results were compared with theoretical data to validate the numerical model developed. The simulated three degrees of freedom (3−DoF) (surge, heave, and pitch) of a rectangular floating box have excellent consistency with experimental data. MoorDyn was coupled with DualSPHysics to include a mooring simulation. Finally, we modelled and simulated a real mariculture platform on the coast of China. We simulated the 3−DoF of this mariculture platform under a typical annual wave and a Typhoon Dujuan wave. The motion was light and gentle under the typical annual wave but vigorous under the Typhoon Dujuan wave. Experiments at different tidal water levels revealed an earlier motion response and smaller motion range during the high tide. The results reveal that DualSPHysics combined with MoorDyn is an adaptive scheme to simulate a coupled fluid–solid–mooring system. This work provides support to disaster warning, emergency evacuation, and proper engineering design.

scholarly journals Multiscale Boundary Element Method for Acoustic Wave Model

MATEMATIKA ◽  
2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Nor Afifah Hanim Zulkefli ◽  
Yeak Su Hoe ◽  
Munira Ismail
Keyword(s):  
Boundary Element Method ◽  
Numerical Methods ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Computational Efficiency ◽  
Large Scale ◽  
Wave Model ◽  
Large Scale Problems ◽  
Speed Up ◽  
Element Method

In numerical methods, boundary element method has been widely used to solve acoustic problems. However, it suffers from certain drawbacks in terms of computational efficiency. This prevents the boundary element method from being applied to large-scale problems. This paper presents proposal of a new multiscale technique, coupled with boundary element method to speed up numerical calculations. Numerical example is given to illustrate the efficiency of the proposed method. The solution of the proposed method has been validated with conventional boundary element method and the proposed method is indeed faster in computation.

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