• Title, Summary, Keyword: linear strain triangle

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

  • Ryu, Yong-Hee;Ju, Bu-Seog;Jung, Woo-Young;Limkatanyu, Suchart
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.4 no.1
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    • pp.1-8
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    • 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.

A direct XFEM formulation for modeling of cohesive crack growth in concrete

  • Asferg, J.L.;Poulsen, P.N.;Nielsen, L.O.
    • Computers and Concrete
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    • v.4 no.2
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    • pp.83-100
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    • 2007
  • Applying a direct formulation for the enrichment of the displacement field an extended finite element (XFEM) scheme for modeling of cohesive crack growth is developed. Only elements cut by the crack is enriched and the scheme fits within the framework of standard FEM code. The scheme is implemented for the 3-node constant strain triangle (CST) and the 6-node linear strain triangle (LST). Modeling of standard concrete test cases such as fracture in the notched three point beam bending test (TPBT) and in the four point shear beam test (FPSB) illustrates the performance. The XFEM results show good agreement with results obtained by applying standard interface elements in FEM and with experimental results. In conjunction with criteria for crack growth local versus nonlocal computation of the crack growth direction is discussed.

Physical modelling of sliding failure of concrete gravity dam under overloading condition

  • Zhu, Hong-Hu;Yin, Jian-Hua;Dong, Jian-Hua;Zhang, Lin
    • Geomechanics and Engineering
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    • v.2 no.2
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    • pp.89-106
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    • 2010
  • Sliding within the dam foundation is one of the key failure modes of a gravity dam. A two-dimensional (2-D) physical model test has been conducted to study the sliding failure of a concrete gravity dam under overloading conditions. This model dam was instrumented with strain rosettes, linear variable displacement transformers (LVDTs), and embedded fiber Bragg grating (FBG) sensing bars. The surface and internal displacements of the dam structure and the strain distributions on the dam body were measured with high accuracy. The setup of the model with instrumentation is described and the monitoring data are presented and analyzed in this paper. The deformation process and failure mechanism of dam sliding within the rock foundation are investigated based on the test results. It is found that the horizontal displacements at the toe and heel indicate the dam stability condition. During overloading, the cracking zone in the foundation can be simplified as a triangle with gradually increased height and vertex angle.

The stress analysis of a shear wall with matrix displacement method

  • Ergun, Mustafa;Ates, Sevket
    • Structural Engineering and Mechanics
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    • v.53 no.2
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    • pp.205-226
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    • 2015
  • Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

Fluid-structure interaction system predicting both internal pore pressure and outside hydrodynamic pressure

  • Hadzalic, Emina;Ibrahimbegovic, Adnan;Dolarevic, Samir
    • Coupled systems mechanics
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    • v.7 no.6
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    • pp.649-668
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    • 2018
  • In this paper, we present a numerical model for fluid-structure interaction between structure built of porous media and acoustic fluid, which provides both pore pressure inside porous media and hydrodynamic pressures and hydrodynamic forces exerted on the upstream face of the structure in an unified manner and simplifies fluid-structure interaction problems. The first original feature of the proposed model concerns the structure built of saturated porous medium whose response is obtained with coupled discrete beam lattice model, which is based on Voronoi cell representation with cohesive links as linear elastic Timoshenko beam finite elements. The motion of the pore fluid is governed by Darcy's law, and the coupling between the solid phase and the pore fluid is introduced in the model through Biot's porous media theory. The pore pressure field is discretized with CST (Constant Strain Triangle) finite elements, which coincide with Delaunay triangles. By exploiting Hammer quadrature rule for numerical integration on CST elements, and duality property between Voronoi diagram and Delaunay triangulation, the numerical implementation of the coupling results with an additional pore pressure degree of freedom placed at each node of a Timoshenko beam finite element. The second original point of the model concerns the motion of the outside fluid which is modeled with mixed displacement/pressure based formulation. The chosen finite element representations of the structure response and the outside fluid motion ensures for the structure and fluid finite elements to be connected directly at the common nodes at the fluid-structure interface, because they share both the displacement and the pressure degrees of freedom. Numerical simulations presented in this paper show an excellent agreement between the numerically obtained results and the analytical solutions.