• Title/Summary/Keyword: Finite Elements

검색결과 2,687건 처리시간 0.028초

A simple limit analysis procedure for reinforced concrete slabs using rigid finite elements

  • Ahmed, H.;Gilbert, M.
    • Structural Engineering and Mechanics
    • /
    • 제84권1호
    • /
    • pp.129-141
    • /
    • 2022
  • It has previously been proposed that the yield-line method of analysis for reinforced concrete slabs could be automated via the use of rigid finite elements, assuming all deformations occur along element edges. However, the solutions obtained using this approach can be observed to be highly sensitive to mesh topology. To address this, a revised formulation that incorporates modified yield criteria to account for the presence of non-zero shear forces at interfaces between elements is proposed. The resulting formulation remains simple, with linear programming (LP) still used to obtain solutions for problems involving Johansen's square yield criteria. The results obtained are shown to agree well with literature solutions for various slab problems involving uniform loading and a range of geometries and boundary conditions.

Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석 (Numerical Evaluation of Fundamental Finite Element Models in Bar and Beam Structures)

  • 류용희;주부석;정우영
    • 복합신소재구조학회 논문집
    • /
    • 제4권1호
    • /
    • pp.1-8
    • /
    • 2013
  • The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

유한요소법에 의한 이차원연속체의 구조해석 (Structural Analysis of Two-dimensional Continuum by Finite Element Method)

  • 이재영;고재군
    • 한국농공학회지
    • /
    • 제22권2호
    • /
    • pp.83-100
    • /
    • 1980
  • This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.

  • PDF

Parametric study of piled raft for three load-patterns

  • Sawant, V.A.;Pawar, S.V.;Ladhane, K.B.
    • Coupled systems mechanics
    • /
    • 제1권2호
    • /
    • pp.115-131
    • /
    • 2012
  • Paper presents an improved solution algorithm based on Finite Element Method to analyse piled raft foundation. Piles are modelled as beam elements with soil springs. Finite element analysis of raft is based on the classical theory of thick plates resting on Winkler foundation that accounts for the transverse shear deformation of the plate. Four node, isoparametric rectangular elements with three degrees of freedom per node are considered in the development of finite element formulation. Independent bilinear shape functions are assumed for displacement and rotational degrees of freedom. Effect of raft thickness, soil modulus and load pattern on the response is considered. Significant improvement in the settlements and moments in the raft is observed.

Application of graded harmonic FE in the analysis of 2D-FGM axisymmetric structures

  • Karakas, Ali I.;Daloglu, Ayse T.
    • Structural Engineering and Mechanics
    • /
    • 제55권3호
    • /
    • pp.473-494
    • /
    • 2015
  • A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

유한요소법에 의한 펌프축계의 안정성해석 (Stability analysis of pump using finite element method)

  • 양보석
    • Journal of Advanced Marine Engineering and Technology
    • /
    • 제10권4호
    • /
    • pp.31-40
    • /
    • 1986
  • With the tendency toward high speed and high pressure in centrifugal pumps, the problem of sub-synchronous vibration has arisen, caused by the hydraulic forces of the working fluid, such as wearring, balance piston, impeller, etc.. These forces can drastically alter the rotor critical speeds and stability characteristics, and can be acted significant destabilizing forces. For preventing such self-excited vibration, the desing of the rotor system needs, which would secure the stability of the machine. In this paper, a procedure is presented for dynamic modeling of rotor-bearing-seal-impeller systems which consist of rigid disks, distributed parameter finite rotor elements and discrete bearings, seals and impellers. A finite element model including the effects of rotatory inertia and gyroscopic moments is developed using the consistent matrix approach. The technique of dynamic matrix reduction is applied to the shaft matrices to reduce them to a set of matrices of dynamic of significantly fewer degrees of freedom. The representation of bearing, seal and impeller elements is in term of linearized stiffness and damping matrices by reasonably small perturbations from equilibrium. The stability behavior of a typical double suction centrifugal pump is presented. Results show the influence of clearance and flow conditions on running speeds and stability characteristics.

  • PDF

Analysis of the dynamical behavior of piezoceramic actuators using piezoelectric isogeometric finite elements

  • Willberg, Christian
    • Advances in Computational Design
    • /
    • 제1권1호
    • /
    • pp.37-60
    • /
    • 2016
  • In this paper an electromechanically coupled isogeometric finite element is utilized to analyse Lamb wave excitation with piezoceramic actuators. An effective actuator design reduces the energy needed for Lamb wave excitation, which is beneficial if a structural health monitoring system should be applied for a structure. For a better understanding of the actuator behavior the piezoeceramics are studied both free and bonded at a structure. The numerical part of the analysis is performed utilizing isogeometric finite elements. To obtain the optimal performance for the numerical analysis the effect of k-refinement of the isogeometric element with respect to the convergence is studied and discussed. The optimal numerical setup with the best convergence rate is proposed and is validated with free piezoeceramic actuators. The validated model is then utilized to study the impact of actuator shape and adhesive bondline effect to the wave amplitude. The study shows that simplified analytical equations do not predict the optimal excitation frequencies for all piezoceramic designs accurately.

LONG PATHS IN THE DISTANCE GRAPH OVER LARGE SUBSETS OF VECTOR SPACES OVER FINITE FIELDS

  • BENNETT, MICHAEL;CHAPMAN, JEREMY;COVERT, DAVID;HART, DERRICK;IOSEVICH, ALEX;PAKIANATHAN, JONATHAN
    • 대한수학회지
    • /
    • 제53권1호
    • /
    • pp.115-126
    • /
    • 2016
  • Let $E{\subset}{\mathbb{F}}^d_q$, the d-dimensional vector space over the finite field with q elements. Construct a graph, called the distance graph of E, by letting the vertices be the elements of E and connect a pair of vertices corresponding to vectors x, y 2 E by an edge if ${\parallel}x-y{\parallel}:=(x_1-y_1)^2+{\cdots}+(x_d-y_d)^2=1$. We shall prove that the non-overlapping chains of length k, with k in an appropriate range, are uniformly distributed in the sense that the number of these chains equals the statistically correct number, $1{\cdot}{\mid}E{\mid}^{k+1}q^{-k}$ plus a much smaller remainder.

이차원 하이브리드 특별 요소을 이용한 균열을 내포하는 용접점의 파단 해석 (Fracture analysis of spot-welds with an edge crack using 2-D hybrid special finite element)

  • 양춘휘;송정한;허훈
    • 한국소성가공학회:학술대회논문집
    • /
    • 한국소성가공학회 2004년도 춘계학술대회 논문집
    • /
    • pp.39-42
    • /
    • 2004
  • In the present paper, a novel systematic method using the 2-D hybrid special finite elements containing an edge crack is employed to study the fracture behaviors of laser beam spot-welds in automotive structures. 2-D hybrid special finite elements each containing an edge crack can assure the high precision especially in the vicinity of crack tips and give a better description of its singularity with only one hybrid element surrounding one crack. Therefore, the numerical modeling of the laser beam spot-welds can be greatly simplified. Some numerical examples are provided to demonstrate the validity and versatility of the proposed method. All the lap-shear, lap-tension and angle clip specimens are analyzed and some useful fracture parameters (such as stress intensity factors, the initial direction of crack growth) are obtained simultaneously.

  • PDF

Nonlinear finite element analysis of fibre reinforced concrete deep beams

  • Swaddiwudhipong, S.
    • Structural Engineering and Mechanics
    • /
    • 제4권4호
    • /
    • pp.437-450
    • /
    • 1996
  • A study on the behaviour of fibre reinforced concrete deep beams with and without web openings is carried out using nonlinear finite element analysis. Eight node isoparametric plane stress elements are employed to model the fibre reinforced concrete materials. Steel bars are treated using a compatible three node truss elements. The constitutive equations for fibre reinforced concrete materials take into account the softening effect of co-existing shear strains. Element stiffness at each step is formulated based on the tangent modulus at the current level of principal strains. Transformation between principal directions and global coordinate system is imposed. Comparison of analytical results with experimental values indicates reasonably good agreement. The proposed numerical model can be used to study the behaviour of this composite structures of practically any geometries.