EAT 353 STRUCTURAL ANALYSIS II INTRODUCTION TO FINITE

EAT 353 STRUCTURAL ANALYSIS II INTRODUCTION TO FINITE ELEMENT ILYA BINTI JOOHARI

Lesson Outcome EXPLAIN the introduction to the finite elements method and their application in structural engineering. APPLY finite element in practical lab in modeling of FE using computer software package

Introduction Engineers model physical phenomena. Analytical descriptions of physical phenomena and processes are called mathematical models. o Developed using assumptions on the process. o Often characterized by differential and/or integral equations. Numerical methods are typically used to solve engineering mathematical models – referred to as numerical simulation.

Finite Element Method (FEM) Finite element method (FEM) is a numerical procedure for solving mathematical models numerically. FEM uses discretization (nodes and elements) to model the engineering system, i. e. , subdivide the problem system into small components or pieces called elements and the elements are comprised of nodes. Approximations are introduced over each element to represent the behaviour of the unknown variables.

FEM (cont. ) Different types of elements are available. Accuracy of the finite element approximation is improved by using more elements to approximate the engineering system and/or elements that involve more nodes to define the unknown function(s) variation over the element, e. g. ,

FEM (cont. ) The finite element method (FEM) is a numerical method for solving problems of engineering and it is very helpful in understanding whether or not something will fail without actually having to build it. It does not require as many simplifications and assumptions because it accounts for complexities of geometry, materials and loading. So it is more useful as a real world tool and has become pretty much standard in the construction industry.

Application in Structural Engineering Collapse of RC high-rise building subjected to earthquake

Application in Structural Engineering Fire induced progressive collapse of RC frame

Application in Structural Engineering Earthquake-induced collapse of super large-span cablestayed bridge

Application in Structural Engineering Overload induced collapse simulation for a bridge

Application in Structural Engineering Overload induced collapse of bridge

Applications of Finite Element Analysis In mechanics of materials it is used for structures and trusses. It is used to understand to prevent how some structures are going to behave under the action of some loads. For a bridge, how is it going to behave with the vibrations, or with the effect of the air, or with the variations of temperature. The aircraft industry uses this method to determine the static and dynamic answer of planes and space crafts to the great variety of environments and conditions that can be found during their operation. In the case of mechanics of fluids, the method is used to know how a wing of a plane is going to behave with the air flux passing through it. For heat transfer, it allows to know how a turbine is going to behave, and how the material is going to be affected for the effect of the heat.

Advantages Modelling of complex geometries and irregular shapes are easier as varieties of finite elements are available for discretization of domain. Boundary conditions can be easily incorporated in FEM. Different types of material properties can be easily accommodated in modelling from element to element or even within an element. The systematic generality of FEM procedure makes it a powerful and versatile tool for a wide range of problems. FEM is simple, compact and result-oriented and hence widely popular among engineering community.

Advantages (Cont. ) FEM can be easily coupled with computer-aided design (CAD) programs in various streams of engineering. An FEM model can be developed at different levels and it is possible to interpret the method in physical terms. Availability of large number of computer software packages and literature makes FEM a versatile and powerful numerical method.

Disadvantages Large amount of data is required as input for the mesh used in terms of nodal connectivity and other parameters depending on the problem. Generally, voluminous output data must be analysed and interpreted. Experience, good engineering judgment and understanding of the physical problems are required in FEM modelling. Poor selection of element type or discretization may lead to faulty results.

FEM Analytical Procedure 1 2 3 • Divide the structure into finite elements. • Mesh generation programs, call preprocessors, help the user in doing this work. • Formulation the properties of each element. In stress analysis, this means determining nodal loads associated with all element deformation states that are allowed. • Assemble elements to obtain the finite element model of the structure.

4 5 6 7 8 • Apply the known loads: nodal forces and/or moments in stress analysis • In stress analysis, specify how the structure is supported. This step involves specifying the known nodal displacements, which are often zero. • Solve simultaneous linear algebraic equations to determine nodal degrees of freedom (DOF) – displacements for stress analysis. • In stress analysis, calculate element strains for the nodal DOF and the element displacement interpolation field so that the element stresses can be calculated from the element strains. • Output interpretation programs, call postprocessors, help the user sort the output and display it in graphical form.

Finite Element Method Using Computer Software

Typical FEM Procedure Using Commercial Software

FEM Procedure

FEM Procedure (Cont. )

FEM Procedure (Cont. )

Mistakes by Users Elements are of the wrong type o e. g. Shell elements are used where solid elements are needed Distorted elements Supports are insufficient to prevent all rigid – body motions Inconsistent units (e. g. E = 200 GPa, Force = 100 lbs. ) Too large stiffness difference – Numerical difficulties

Common FEM Software Abaqus: Franco-American software from SIMULIA, owned by Dassault Systemes ANSYS: American software LUSAS: UK Software Plaxis: Geotechnical 2 D/3 D FE suites, with support for stresses, deformations, groundwater flow and dynamics. SAP 2000: American software

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