3D-finite Element Analysis of Beam Design

3D-finite Element Analysis of impart figure of speechAbstract some(prenominal)ly design and development activities involves in huge amount of time and funds in bringing start the final product to the market, whilst functionality of the product organism crucial under all scenarios without fail or malfunctioning everyplace a period of time.Earlier design was carried out by the conventional regularitys from planning to final manufacturing of a percentages and the conduct of the product was understood moreover when it was non meeting its functionality.Recent developments in the above said cranial orbit is vast, as this enables an engineer to study the sort of a destiny/ convocation, long whist suggesting precautionary measures or a possible solution in clear the member thereby pull rounds an system time and effort.Thanks to the youthful developments in the field of Stress analysis, along with the CAD packages, which genuinely enable us to visualize the component in 3 D and analysis and design, validate it to begin with it is actually released for manufacturing. raisemore the robustness of CAE packages enables us to visualize the behavior of the component/assembly when it is actually put to work defining constrains under which it has to perform.Industries powerfully rely on these packages to reduce the time and money involvement of a comp each and it is important for an Engineer to adapt the methods presented in this paper in the right approach so as to meet the design criteria which should be practical in nature.IntroductionThis paper demonstrates the Design of a broadcast which has to be validated under several constrains/operating conditions, and understanding its behavior under these real time situations.Application of Stress methods exploitation consentaneous Works Simulation package is demonstrated to understand the behavior of the calamus.3D Finite chemical element analysis is one of the approaches in understanding the behavior of th e load caterpillar treads under different situations and with different frontier conditions.Several diversify sub variances argon validated to design the best propagate under the given load conditions and the best beam based on several criteria ar made, by demonstrating several plots.Hand/Theoretical calculations and resultants from Simulation atomic number 18 interpret in straddle to study the behavior of the beam.Methods of this Stress Simulation and pertinent steps are explained by plotting various plots interchangeable the Stress, Displacement and performer of Safety by relevant comments at certain stages are through with(p) for the company to understand the process and design validation.Further it is important for the preventative engineer to understand the usage of 3D finite element method so as to interpret the results and to make design changes before the component being put it function.Beam analysis Part 1The figure below shows the beam on which the gobs a re acting at principals P1, P2 and P3 of magnitude 18KN, 26KN and 20KN respectively.Beam 1 and 2 are bolted with pins through the cardinal beams and the beam is support at two locations. Analyzing the above situation, several considerations are needed in order to apply and analyze the situation. The above situation is a slip of s think of supported beams at either ends and loaded at the center.Design phaseThe given discussion dents are designed victimization secure whole caboodle package as per the dimensions provided.The get over-sectional of beams designed is plotted below.Consider the tangle-section 1 for analysis.Below shows the scratch-section 1 with dimensions being A= 0.3m, B=0.3m respectively.3D element significant element type analysis using finite element methodCross-section 1 Beam with circular holeAs shown above the assembly is created using solid work as Solidworks.asm stage and is meshed and analysis is carried out. Several steps are carried out like con strains, load conditions, designate significant are done in order to study the behavior of the assembly.Load loads are defined at collar locations as shown either of the beams is connected by means of metal pads of 3mm slow with pins to support them. As we apply the loads at points P1, P2 and P3, simulation is carried out and a report on the desired results is obtained and are plotted below.Further to the design of the beam with relevant dimensions, simulation of the assembly is carried out using Solid works simulation. Several boundary conditions are implied, like the loads at the given locations, applying material, bolts at four locations and finally meshing the assembly to perform the analysis.Repeating the above procedure for rest of the gravel-sections for design of beam, succeeding(a) plots will account for the values of Von-misses mark, version and factor of sentry go.Deflection CalculationsFrom the plication moment diagram, we observe that the utmost deflection o ccurs at the centre of the beam. The maximum load due to all the 3 loads can be piece out. By using the Principle of Superposition, the deflection due to each load can be interpolated to the centre.Consider a load P acting on a beam AB at a distance of a from end A as shown in figure. The warp moment plot shown in figure above, shows a discontinuity at the point x=a.Solving for each of the lengths of the beamFor length AD,(d2y /dx2) = (M/EI) = (Pbx/EIL) 1 integrating equation 1, we fail,y = (Pbx3/6EIL)For length DB,y = (Pax3/2EI) (Pax3/6EIL) + B1x + B2To determine the four constants A1 and A2, two boundary conditions and two continuity conditions are employ.For segment AD, y (0) = 0 = A2For segment DB,y (L) = 0 = (PaL2/3EI) + B1L + B2Equating the deflections and slope on twain segments at x=a, and solving the four equations, we get,A1 = (Pb/6EIL) (L2 b2)A1 = 0B1 = (Pa/6EIL) (2L2 + a2)B2 = (Pa3/6EI)Hence we get the following equation, for length ADy = (Pbx/6EIL) (x2 L2 + b2) . (2)Considering the load P1 = 18KN, the deflection at mid(prenominal)point, we have,P = 18000N, x = 1.4m, b = 1.9m, L = 2.8m, E = 220 X 109N/m2. exchange these values in equation (2), we gety = (2.9407 X 10-8) / I mHence, below are the valuesFor cross section 1 y1circle = 0.04523mmFor cross section 2 y1oct = 0.0454mmFor cross section 3 y1sqr = 0.0465mmFor cross section 4 y1isect = 0.06022mmFor segment AD, using the expressions obtained for B1 and B2 in the deflection equation, we get,y = (Pa/6EIL) (x3/2) (x3/6L) x (2L2 + a2)/6L + (a2/6) 2Considering the load P2 = 20KN, deflection at mid point can be calculated using,P = 20000N, x = 1.4m, a = 1.7m, L = 2.8m, E = 220 X 109 N/m2.Substituting the above values in equation (2), the deflection at mid point D is found to bey = (2.2074 X 10-8)/I mHence,For cross section 1 y2circle = 0.03395mmFor cross section 2 y2oct = 0.0341mmFor cross section 3 y2sqr = 0.0349mmFor cross section 4 y2isect = 0.0452mmSimilarly, considering the load P 3 = 26000N, deflection at mid point is,y = (54.0484 X 10-9)/I mHence,For cross section 1 y3circle = 0.0831mmFor cross section 2 y3oct = 0.0835mmFor cross section 3 y3sqr = 0.0854mmFor cross section 4 y3isect = 0.1107mmTotal deflection is given byy = y1 + y2 + y3Hence,For cross section 1 y = 0.1622mmFor cross section 2 y = 0.1630mmFor cross section 3 y = 0.1668mmFor cross section 4 y = 0.2161mm gene of safety for the beams.Factor of safety is given by the formulaFOS = ?yield / ?maxGiven, yield melodic line of the material, ?yield = 650N/mm2Using the above data, we get,For cross section 1 FOS = (650/8.6) = 75.58For cross section 2 FOS = (650/8.64) = 75.23For cross section 3 FOS = (650/8.84) = 73.53For cross section 4 FOS = (650/11.46) = 56.72By the above results, the cross section with the highest FOS can be chosen for designing the beam. Hence it can be recommended to choose the cross section with circular hole for final design.Part 2The regularize is red color is critical, means i t has high stress and displacement. Hence clamping use will play a major role.From the plot, the maximum displacement at this location is 0.6511 mm, which is less than the customers expectations and hence the design is safe.As this displacement is intimately 3.8 times of the specified value 2.5mm, no design changes or precautions would be needed. Therefore,Maximum displacement Specified value.Part 3Finite element method is one of the methods widely used and applied among the industries in the recent years and is used to study the behavior of the part by assigning various properties on to it.Method of simulationStatic studies in Solid works simulation calculate displacements, reaction forces, strains, stresses, failure criterion, factor of safety, and shift estimates. Available loading conditions include point, line, surface, acceleration (volume) and thermal loads are functional.Below criteria are important and are followed in this document so as to obtain values which are reali stic in natureThe approach is done in three phases and are,Bottom up assembly-Phase 1Defining load points-Phase 2Simulation-Phase 3Phase 1.Assembly of beams with relevant dimensions was done with fully defining the sketch geometry.Generating bosses with desired lengths and creating the profile as needed.Mates being defined between each parts using mate options in assembly mode.Phase 2.Split of 10mm was done at the top surface of the beam was done in order to imply point loads.Phase 3.Solid works simulation tool was used to access the simulation options.Steel was applied from the material database for all the components in the assembly.Connections were defined so as to make the assembly a pissed structure by defining the locations and this creates an effect of holding both the beams by means of bolts.Fixtures create an effect of holding the beam as required and are done at the either ends.Loads in call of Newton were applied on to the points which were defined at phase 2. lucre s urface was defined for the entire assembly and this inturn divides the geometry and several nodes are created for analysis. ultimately the meshed model will provide us the study report, Von-misses stress, Factor of safety and Displacement of all the four cross-sections are obtained.Possible mis larns in simulationIt is up to the safety engineer in order to take extreme care before the analysis is performed so as to repress the failure or in faithful results during or before the simulation is actually performed. Mistakes should be avoided to the maximum extent while conducting simulation, as this might twist the results and are not practical in nature and hence go away to misinterpretation.Some of them are listed below.Applying the material This result in wrong stress and strain plots, displacement plots, Factor of safety, this inturn results in wrong load path distribution.Defining boundary conditions Defining boundary conditions is crucial in price of accurate results. Loadings should be done as per the real situation and thrown-away(prenominal) assumptions have to be avoided.Generating mesh Applying mesh is one of the important criteria as this procedure being the base on which the elements of the member or the beam is divided into several millions of individual pieces and are analyzed by applying degrees of freedom. cyberspace size Mesh size is important in order the material/component to take the load conditions. Larger mesh could result in teeny-weenyer deflection and results may not be practical in nature.Clamping face Wrong clamping face in simulation would completely demasculinize the end result and this leads in wrong interpretation of the results obtained from the stress plot, displacement plots and Factor of safety.Mesh sizes and typesSolid works simulation currently includes solid continuum elements, curved surface shell elements (thin and thick) and truss and frame line elements. The shells are triangular with three vertex nodes or three v ertex and three mid-edge nodes. Solids are tetrahedral with four vertex nodes or four vertex and hexad mid-edge nodes. They use additive and quadratic interpolation for the solution based on whether they have two or three nodes on an edge. The linear elements are alike called simplex elements because their number of vertices is one more than the dimension of the space. The size of each element indicates a region where the solution is approximated by a spatial multinomial. Most finite element systems, including SW Simulation, use linear or quadratic complete polynomials in each element. You can promise by inspection which is being used by looking at an element edge. If that line has two nodes the polynomial is linear.If it has three nodes then the polynomial is quadratic.When the model is set for simulation, the program sub-divides the model into many tetrahedral small elements, these small points share a common point called as NODE. Below shows the small element where a common n ode is shared by curves, lines and edges. going away between hand calculation and simulationFew difference do exists between theoretical and hand calculations.Hand calculations Hand calculations are a lot called as theoretical calculations, because of the fact that it does not take into consideration of several constrains could not be defined as we could do it in simulations. actual cannot be assigned in hand calculations.Mesh cannot be created for damp and accurate result.Deflection, stress plot, displacement plots could not be visualized in hand calculations.Several assumptions might be required and thereby accounts in the deviation of the result from that of simulation.Hand calculations are based on the available formulae like from the design data hand book and are not different compared to simulation results.Result analysis like the animation of the result and high stress regions could not be obtained from hand calculations.Changes in boundary conditions would require repeatin g the procedure in hand calculations and time overpowering process.ConclusionStudy of 3D-Finite element analysis of beam design assembly, direct the capabilities of simulation. The idea of using the presented methods and techniques helps in optimizing the product before manufactured.This helps an industry in being changing their design at this stage based on the results obtained from simulation. Simple to complex parts/assemblies are simulated by this method, by defining several boundary conditions.The advancement in FEA area is vast, and has the capabilities of creating an surroundings of real time engineering situation and much finer results could also be obtained, as it provides options for finer mesh and hence more accurate the results.Finally this method of optimizing or validating the product at the initial level before design is done, has its own advantages, whilst it is worth understanding the customers requisite along with understanding the basic concepts of FEA makes a worth effort towards any engineering problem.Hence I strongly suggest for any organization to follow the process of FEA and get the full benefit of the same, as they could save time in the process of optimization of the product.ReferencesClass tutorial.S Timo shenko and D H young. 5th Edition. Elements of strength of materials. vividness of materials by Bela I. Sandor.Solid works study material.Strength of materials by Ferdinand L. Singer and Andrew Pytel, 3rd EditionStrength of materials by Surya Patnaik and Dale Hopkins, Title A new unified theory for the twenty-first century.