The finite element method (FEM) is one of the most known simulation method that estimate and analysis behaviour of system and structure in defining conditions. Researchers work has been finished in the field of numerical modelling in the last twenty years ago that provide engineers today to predict the simulations very close to real problem. Hence, nonlinear phenomena have existed standard modelling task in structural phenomena such as nonlinear material behaviour, deformation, contact problems. The result of the development of the software technology, simulations performs with millions of freedoms and eliminate the time consuming and cost.
CONTENTS
1. INTRODUCTION
2. TASK1 LINEAR ANALYSIS AND MODEL UPDATING
Table 2.1: Material Properties for Shear Frame
Figure 2.2: Geometry of Three storey Shear Frame
Graphic 2.3: Experimental results for Natural frequency
2.1 SIMULATION
Figure 2.4: Defining Material Properties in ANSYS
Table 2.5: Geometry Dimensions
Figure 2.6: Structural Displacements and Meshing
2.2. RESULTS AND DISCUSIIONS
Table 2.3.1: Result of the Frequency both ANSYS and Experimental
Figure2.3.2: Mode shapes and Frequencies
Table 2.3.3: Result of the Frequency both ANSYS and Experimental after Model Updating
Figure2.3.4: Mode shapes and Frequencies after Model Updating
3. Task2 MATERIAL NONLINEAR PROBLEM
Figure 3.1: Structure Geometry
Table 3.2: Materials Properties
3.1. Simulation
Figure 3.3: Material properties for each material
Table 3.4: Key points numbers and coordinates
Figure 3.5: Model of the structure by ANSYS
Figure 3.6: Loads on the structure and Meshing
Figure 3.7: Convergence of the Solution
3.2Result and Discussion
Figure 3.8: Example of the incremental methods (Autodesk, 2014)
Figure 3.9: Von Mises Elastic strain and Stress Intensity
Figure 3.10: Maximum Displacement
CONCULSION
REFERENCES
1. INTRODUCTION
The finite element method (FEM) is one of the most known simulation method that estimate and analysis behaviour of system and structure in defining conditions. Researchers work has been finished in the field of numerical modelling in the last twenty years ago that provide engineers today to predict the simulations very close to real problem. Hence, nonlinear phenomena have existed standard modelling task in structural phenomena such as nonlinear material behaviour, deformation, contact problems. The result of the development of the software technology, simulations performs with millions of freedoms and eliminate the time consuming and cost (Erke w. et all, 2002).
The majority of structural dynamics problems characterise behaviour of system are illustrated in the terms of the following matrix equations;
[M]{ü} +[B]{Ci} +[K]{u} ={Fe(t)} (1)
In the equation (1) is illustrated that M, c and к symbolize the structural mass, damping and stiffness matrices respectively. Moreover, Ü, Ù and и are the vectors of the nodal accelerations, velocities, and displacements respectively. Lastly, the vector of the applied forces can be shown as F(t) (Robert N., 2016).
The nonlinear problem can be occasioned by some various reasons. It can be observed in ordinary structures such as plates, beams, as a result of buckling and large deformation related effects. For instance, the typical nonlinear problem is the aircrafts that are backlash and friction in the control of surface, joints, stiffening nonlinearities in the engine to wing structure (Gaétan К.,2002).
Finite Element solutions can be ensured by using ANSYS software for most of the engineering disciplines such as static, dynamics, heat flow, fluid, electromagnetic, also coupled field problems. Moreover, the ANSYS users can be run both linear and nonlinear problems where structural nonlinearities can occur because of nonlinear material behaviour, deformations or conduct boundary conditions (Erke w. et all, 2002).
This assignment report includes the following two task, In Task1 is related with linear analyses and model updating. Shear frame can be modelling in the ANSYS and then can be added mass in the existing structure. Moreover, it will be compared two results that are experimental results of the natural frequency and simulation results of the natural frequency that obtain in the ANSYS. In the Task2 is about material nonlinear problem that is structure is made of aluminium, brass and copper. The structure is simply supported along the base lines with both ends and load distribution is applied 0.8m away from the end A. Hence, the bilinear model properties are applied in the modelling. After the modelling, stress and strain relationship will be discuss in the following chapter.
2. TASK1 LINEAR ANALYSIS AND MODEL UPDATING
In this task, finite element model of three storey shear frame is created which made of steel of which typical mechanical properties are given in Table 2.1.
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Table 2.1: Material Properties for Shear Frame
A schematic of the structure with dimensions is shown in Figure 2.2. Furthermore, natural frequency and mode shape is analysed in this geometry to get closer results for experimental results that illustrated below in Graphic 2.3.
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Figure 2.2: Geometry of Three Storey Shear Frame
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Graphic 2.3: Experimental results for Natural frequency
2.1 SIMULATION
Simulation is performed following steps using ANSYS Mechanical ADPL software. The steps are;
Step 1Structural Type: the preference is selected as structural.
Step 2Choosing Element: In this modelling SOLID186 is chosen as element type by Preprocessor > Element Type > Add/Edit/ Delete >Add as Solid & 20 node 186. SOLIDI86 is a advanced order 3D 20node solid element that shows quadratic displacement behaviour. Hence, this element is characterized by 20 nodes and each node has three degrees of freedom and per node in the nodal X, y, and z directions (ANSYS, 2013)
Step 3 Defining material properties: Material properties is given in the Table 2.1. These parameters are defined in the simulation by Material Model>Structural>Linear>Elastic>lsotropic and Material Model>Structural>Density
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Figure 2.4: Defining Material Properties in ANSYS
Step 4 Geometry Modelling: The geometry is done by creating volume by
Modelling>Create>Areas>Volumes>Block>By Dimensions as dimension is illustrated in Table 2.5A. After creating the main volume, other volumes are subtracted in the main volume by Modelling>Operate>Booleans>Subtracts>Volumes. The following table 2.5 shows that dimension of main volume in A and subtracted volumes are shown in B, c and D respectively.
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Table 2.5: Geometry Dimensions
Step 5 Meshing: Meshing is obtained by using smart size meshing that level size is 8 for whole structure of the geometry by Meshing>SizeCntrls>SmartSize>Basic and Mesh>Volumes>Free and (select pick all the volume).
Step 6 Define the Loads: The structure is supported along the base areas both the legs. Therefore, all degree of freedom is constrained along the base areas by Solution>Define Loads>Apply>Displacement>On Areas
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Figure 2.6: Structural Displacements and Meshing
2.2. RESULTS AND DISCUSIIONS
After setting all parameters in the ANSYS, solution type is chosen as a Modal by Solution>Analysis Type>New Analysis and Analysis option is applied in the ANSYS by Solution Analysis Type>Analysis Options.
Following Table 2.3.1 is shown that the natural frequencies that obtain by ANSYS are higher than experimental values. Hence, the variation of the frequencies is huge enough from the first frequency to third frequency is about 88%, 43% and 13% respectively. That’s why, model must be modify as adding structural mass on the geometry. Since, in the real situation, shear frame has hokes on the body so the results are large than experimental ones.
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Table 2.3.1: Result of the Frequency both ANSYS and Experimental
The following Figures 2,3.2 shows mode shapes of the shear frame and frequencies.
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Figure2.3.2: Mode shapes and Frequencies
Step 7Model Updating: 3D structural mass is defined in the ANSYS by Preprocessor > Element Type > Add/Edit/ Delete >Add structural mass 3D mass 21. After that, weight of the mass is defined each direction is about 0.82 kg.
Following Table 2.3.1 is shown that the natural frequencies for each modes that obtain by ANSYS software are close to experimental results. Hence, these ANSYS results are more realistic than without mass addition. Moreover, the variation of the frequencies from the first one to third one is about 4%, 10 %־ and %1 respectively. During the simulation, different mass weight and different locations are performed. There are two points that effect the results during the simulation. The first point is that, while weight of the mass is increasing, the frequencies are decreasing. The other point is that, results are changing where to add mass on the structure. Therefore, if the model of the structure is same as real shear frame, the frequencies results for all nodes will be much more closer to experimental results than existing results by ANSYS.
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Table 2.3.3: Result of the Frequency both ANSYS and Experimental after Model Updating
The following Figures 2,3.4 shows mode shapes of the shear frame and frequencies.
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Figure2.3.4: Mode shapes and Frequencies after Model Updating
3. TASK2 MATERIAL NONLINEAR PROBLEM
The structure is illustrated as in Figure 3.1 that is made of aluminium, brass and copper. The structure is simply supported along the base lines with both ends and load distribution is applied 0.8m away from the end A. Following table 3.2 is illustrated that material properties is belong to structure. Therefore, different materials are used in the structure that means that problem is related with material nonlinearity.
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Figure 3.1: Structure Geometry
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Table 3.2: Materials Properties
Simulation is performed following steps using ANSYS ADPL software. The steps are:
Stepi: The preference selected is structural and the element type is selected as Solid 10 node 187, by Preference>Element Type> Add/Edit/ Delete. SOLID187 is characterised by 10 nodes each node has three degrees of freedom and per node in the nodal X, y, and z directions (ANSYS, 2013)
Step2: The materials are defined separately for three different materials that mention above table 3.2.
i. Preprocessor > Material Props > Material Model > structural > Linear »Elastic > Isotropic. Young’s Modulus and Poisson’s Ratio is defined in this section according to Table 3.2.
ii. Preprocessor > Material Props > Material Model > structural > Nonlinear > Inelastic > Rate Independent > Isotropic Hardening Plasticity > Mises Plasticity > Bilinear. Yield stress and tangent modulus is defined in this section according to Table 3.3
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Figure 3.3: Material properties for each material
Step 3 Geometry: The geometry is done by creating key points, the key points are given in the following Table 3.4.
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Table 3.4: Key points numbers and coordinates
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Figure 3.5: Model of the Structure by ANSYS
After creating the key points, lines are created between the key points. After that, the areas are created separately for each section with connect the lines by Modelling>Create>Areas.>By lines. Finally, all areas are extruded to 0,6 mm in the z direction, by the following comment Modelling>operate>Extrude as shown in Figure 3.5 at final geometry.
Step 4  Mesh: In the geometry, there are three different materials that are copper, brass and aluminium. Therefore, materials are defined in each area by Meshing>Mesh Attribute>Default Attribute according to number of the element that defined in step 2. After defining the materials in the corresponding areas, smart size is used for applying different mesh size in the geometry.
Step 5  Applying Load: Firstly, the structure is simply supported along the base lines both the ends marked A and B. Therefore, all degree of freedom is constrained along the base lines. Secondly, structural loads force is applied the all nodes that located top of the structure. In the program level, only nodal forces are acceptable. Therefore, nodal equivalent loads need to be computed. This can be achieved by defining the loads as a set of statically equivalent loads or manage kinematically equivalent loads. However, for typically load cases that given in the problem, kinematically equivalent loads gives much accurate results than statically equivalent loads (Gambhir ,2011). Hence, In the modelling 5 nodes are chosen and all forces applied equally (200 N) on the structure.
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Figure 3.6: Loads on the structure and Meshing
Step 6 Solution: Before solving the problem, solution controls are applied the program. The maximum number of substeps to be 1000. Hence, if the solution of the program does not converge after the setting steps number, the program stopped. As it can be shown the following figure, the solution is converged.
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Figure 3.7: Convergence of the Solution
3.2Result and Discussion
Nonlinear analysis is involved incremental application of loads. Moreover, loads are not considered at a time generally in calculation, but are gradually increased and solutions to successive equilibrium states are performed. Increment method, ArcLength Method and NewtonRaphson Method, among of these incremental method is used. Hence load vector that given in the problem, is divided into five equal increments. Following Figure 3.8 is illustrated example of the nonlinear process at the incremental method. These values used for nonlinear calculation are displayed.
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Figure 3.8: Example of the incremental methods (Autodesk, 2014)
Moreover, selection of the iteration is established as 10, because it needs to eliminate time consuming and also the result of the accurate that is converged. If the more iteration is chosen in the modelling, it needs to long time for getting the results.
The following Figure 3.9 shows that Von Mises Elastic Strain and Stress Intensity of the structure. According to results, whole structure of the material is in elastic region. Therefore, there is no big plastic deformation on the structure at existing load.
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Figure 3.9: Von Mises Elastic strain and Stress Intensity
The following figure is illustrated that the maximum displacement on the structure is 0,139 e5 m.
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Figure 3.10: Maximum Displacement
Stressstrain curves are significant graphical measure mechanical properties for the materials. Tensile test is one of the most important test technique to obtain stress and strain curve of the material. The engineering measures of the stress and strain are symbolised as σ and τ respectively. Moreover, it can be determinate from the measure of load and deflection using original cross section area and length. Hence, many of the materials carry out Hooke’s law to a make an approximation, so that stress is proportional to strain with the constant of proportionality being the modulus of elasticity or Young’s modulus. When the strain is increased, many materials behaves linear behaviour and, after yield point, material is undergoing the a rearrangement of internal molecular or microstructure to moves new equilibrium stage. This behaviour can be said that plastic regime of the material. The stressstrain curve for brittle materials are typically linear over their full range of strain, eventually terminating in fracture without appreciable plastic flow (David, 2001).
CONCULSION
To sum up, Linear analyses and model updating is applied for given structure in the ANSYS. In order to get reasonable result for experimental values, mass is added the structure. When mass is added in the structure, frequency of the structure is decreased. On the other hand, position of the mass is also highly effected the frequency results. Inside of the adding mass, the other alternative method to change frequency is to be changed the stiffness of the structure. However, this alternative does not used in this simulation.
The conclusion of the task2, material nonlinearity is modelled in the ANSYS with different materials such as, copper, brass and aluminium. Moreover, load is applied with the incremental methods, which is equally applied through the nodes. The analysis is performed under these circumstances.
REFERENCES
ANSYS, Inc, (2013) ANSYS Mechanical APDL Element Reference. USA
Autodesk Knowledge Network (2014) [Online] https://knowledge.autodesk.com/support/robot structuralanalysisproducts/learn explore/caas/CloudHelp/cloudhelp/2014/ENU/Robot/files/GUIDFB3C86D30E3043A682D6 6C50F429FA0Dhtm.html [Accessed 24th March 2017].
David R. (2001) ‘STRESSSTRAIN CURVES’, Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge.
Erke w.,Thomas N. (2002) structural Dynamic Capabilities of ANSYS. Germany: CADFEM GmbH.
Gaétan к. (2002) On the Model Validation in Nonlinear structural Dynamics’ Aspirant F.N.R.S
Gambhir M.L. (2011) Fundamentals of structural Mechanics and Analysis. New Delphi: PHI Learning
Robert N. c. (2016) ‘Structural Dynamics Modelling  Tales of Sin and Redemption’ Measurement Analysis Corporation.

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