Dependability-Based Architectural Scheme Optimization for Functional Purposes - Assignment Example

Name Course Instructor Date Introduction With several physical marvels in engineering and science can be described using partial differentiation equations. In most cases, solving these equations through classical analytical methods for arbitrary shapes is next to impossible. Using the finite element method is one of the statistical approaches through which this partial differential equation can be solved by approximation (Bhutta, et al. p13). From the viewpoint of engineers, the FEM is a method for solving engineering problems such as stress analysis, heat transfer flow of fluids and electromagnetics using computer simulation. It is a fact that smaller deflection is normally obtained by a larger amount of materials. Therefore due to the importance of the weight of the structural materials from an economical point of view, it would be more beneficial if one defines am optimization problem which aims to minimize the weight of the structure simultaneously with minimizing the deflection (Bhutta, et al p13). Material composition is fabricated using a macroscopic combination of two or more constituent materials such that the overall structural characteristics of the composite are superior to the properties of the individual component materials. In Beam construction, high-performance composites are often made from carbon fibers set in an epoxy matrix. The high-performance composite materials exhibit both highly anisotropic strength and stiffness characteristics making the analysis and design of composite structure more challenging. Nevertheless, the anisotropic characteristics of composite materials can also be exploited to obtain tailored structures that meet strict design requirements, yet are lighter that the equivalent metallic structure (Chen et al., p10) This paper aims at using computer aided software to design a perfect and flawless beam. The research uses Finite Element Analysis method. In the recent past, analysis and modeling of composite slabs using the finite element method have been subjected to many researches. However, the result from the study shows that the shear interaction property obtained from the elemental push tests will not produce a result which is satisfactory more so when modified by the response and behavior of the slabs (Bhutta, et al. p13). This paper aims at giving beam modification process and the results. Beam theory The beam theories are normally developed based on a set of assumptions that are used to reduce the complex behavior of a slender, three-dimensional body to an equivalent one-dimensional problem. The importance of the beam theory should be assessed based on its range of applicability, the accuracy of its results and the complexity of the analysis required to obtain an outcome. One of such theories is a homogenization based theory. In this theory, the stiffness properties, shear strain correction matrix and load-dependent corrections within the theory are calibrated based on the hierarchy of solutions called the first states are accurate sectional stress and strain solutions to a series of carefully-chosen (Yi, Sinan, Gengdong Cheng, and Liang Xu et al., 171). One of the classical examples of Beam theory is the Bernoulli-Euler theory. Under this theory, for a beam with its centroidal axis along the x-axis of cross-sectional area, A, the second moment of area (about the y-axis), I, and Young's modulus, E, under the action. This is shown in the diagram below:- In the action of bending moment, M, Shear force, Q, and axial force, P, the resulting displacements are u(x) and w(x) in the x and z-direction respectively. The main assumption for the displacement under this theory is that plane sections initially perpendicular to the centroidal axis remain plane and perpendicular to the axis after deformation. Yi, Sinan, Gengdong Cheng, and Liang Xu et al., (p171) built up an exceptional reason FE method utilizing plane shaft components for examining single and constant traverse composite sections. The techniques fused nonlinear conduct of materials qualities, extra positive minute fortification, the heap slip property for the shear studs and the shear collaboration property between the solid and the steel deck. The malleable load conveying component was utilized as a part of the advancement of the model expecting the fragile bit of the push test information. The conduct of the far reaching stress-strain of the deck was determined unmistakably from the malleable conduct where the relationship was evaluated from flexural tests on the exposed deck. In a review by Chen et al., (p71) the greatest load capacities with regards to the models with unmistakable traverse lengths were appeared to lie along the straight line when plotted on the m-k tomahawks yet additionally fell outside a similar straight line if the steel thickness is changed. This can be credited to the dispersion of the shear stretch which relied on upon the length traverse that did on the section thickness. A review by Chen et al., (p19) on the conduct of the composite chunk with the 2D nonlinear FR utilizing the ABAQUS/Standard module. The sheeting of the steel and the solid were displayed as 2-hub bar components. At that point association between the solid and steel sheeting chunk was then demonstrated with the spring components discharge an arrangement of forced condition between the degrees of flexibility of solid, spring and steel deck shaft components. The property of the spring was then gotten from a piece twisting test. A sloppy break model was utilized for the splitting of the solid while the nonlinear anxiety strain bend was utilized for the steel deck and the pressure of the solid. The constrain slip relationship to reproduce division conduct amongst cement and steel deck in the vertical course that was expected as straight flexible and was likewise displayed with spring components. From the outcomes, the limited component examination was observed to be in great concurrence with full-scale tests for long chunks however belittled the limit of the short pieces. In the process of developing the Finite three-dimensional nonlinear model and analysis, the composite slab was done using the ABAQUS. This was done by text-based files. In the initial development of the model, several properties of the materials particularly the concrete cracking parameters and the nonlinearity of the steel sheeting were tested to help in establishing the suitability of the combination of produced result. Based on the previous studies, several characteristics were chosen. One of the characteristics which were observed was top flange of the steel sheeting (Bhutta et al., p13). The compression and tension property of the steel sheet was assumed in the same process due to the fact the analysis was aiming at reducing the load and load-deflection behavior of the beam. The increased cost of structural material and increase energy consumption is a concern worldwide. Therefore, their consumption and utilization cannot be overlooked by stakeholders. Material handling equipment’s normally uses structural steel for its beam for its operations. For the heavy duty cranes, for instance, using light arms help in saving materials cost as well as trim down consumption of power during its operation. For the configuration and optimization of the twin beam crane arm, the common methodology is refined through direction stipulated in the predominating codes and benchmarks. The outline calibration of crane arm across section was developed by (Yi, Sinan, Gengdong Cheng, and Liang Xu et al., 178). While keeping the cost of the mass as constraints, the ideal configuration of the straightforward symmetrical welded box pillar which is joined by curving anxiety, shear force and clasping imperative parametric and numerical work on load carrying the beam at the single point was done. Gandomi, Amir Hossein, et al. (45) analyzed the quality boundary of networks with rectangular slits, the paper further emphasized on the expectation of anxiety in case of the rectangular section. Bhutta, et al. (p23) measured clasping issue of the trusses in the situation of twin bar crane arms due to welding supporting plates. In the examination of locking and quality of the dainty walled structure, the study has proved very useful. In the case of improvement of the cool structured I-bar and open segment, this is also important in development and improvement of the twin bar beam. For the current design concerning the flimsy walls of the twin bar crane, this is to help in improving the efficiency and cost-effectiveness. Specification of Crane In doing this analysis, data that will be gathered from the industry and the input data for analysis. The data will include geometry and design as will be explained below with the impact on loading Factor which will be 1.25. The type= Gantry Crane Load = 35 ton = 343350 N Loading factor = 1.25 Column Height = 16.01 m = 16010 mm Span = 23 m = 23000 mm The classification of Gantry Crane Classification of beam crane is one of the standards and regulations which are very necessary when it comes to design, and this classification is according to the intensity of the work which the number of cycles designed into parameters. The Gantry cranes, in this case, include heavy cranes and consist of:- Designed cycles (N) 2,000,000 cycles Designed cycles per day (n): 350-500 cycles In the process of optimization of the arm, in this study British standards of 2573 rule for designing cranes was used. The crane was classified as U 7 in the list of classes as shown in the table below:- Class of Utilization Maximum Operation cycles Remarks U 1 3.2 X 104 Infrequent use U 2 6.3 X 104 U 3 1.25 X 105 U 4 2.5 X 105 Fairly Frequent use U 5 5 X 105 Frequent use U 6 1 X 106 Very frequent use U 7 2 X 106 Continuous use U 8 4 X 106 U 9 >4 X 106 Material specification The technical specification and the material of construction that include vital parameters in the analysis of the beam strength structure. The selected material for the arm will be ASTM A 36 having the following properties. Module of elasticity that ranges between 200000 to 210000 Mpa (N/ mm2) The ratio for Poisson’s of 0.26 Tensile strength 775 MN/m2 Yield strength 715 MN/m2 Young’s modulus 72.4 GN/m2 Poisson’s ratio 0.33 Ultimate Strength 460 Mpa (N/mm2) Steel Density 7850 Kg/m3 The specification for the arm A rectangular hollow was used to design the girder profile. The overall structure can be illustrated in the figure below:- Figure 1: Design optimization process The overall girder dimension can be summarized in the table below:- Size Thickness H x B b y t1 t2 mm mm mm mm mm mm 1550 650 600 775 8 16 For the construction of the girder, the following are the required specification Sectional Area Mass/unit A w w Cm2 Kg/m kN/m 465.67 400.78 3.93 Moment of Inertia Radius of the Gyration I xx I yy R xx R yy Cm 4 Cm 4 Cm Cm 1650535 300341 64.72 25.39 The Finite Simulation Analysis By the beam mechanical engineering theories were done. The analysis is based on the finite element method for the analysis to have a more comprehensive results which are then compared with the theoretical results. There were four constant loading carried out, and the results are recorded in the table below:- Load Case Load Ton 1 5 2 15 3 17.5 4 35 The arm modeling process For the twin beam arm, modeling design was done using the Solidworks. The modeled part of the beam was taken through Finite Element Analysis using the same software by assigning a value for the constraints, design variables and goals of two parameters model. The resultant outcome is shown in the figure below. Meshing process was dome with parameters by the content in the table below using the tetrahedron cell type with the resultant in a non-structured smooth mesh. The parameters of the meshing is shown here:- Properties Values Relevance center Fine Element size 250 mm Smoothing Medium Transition Fast Minimum angel length 6 mm Transition ratio 0.2772 Growth 1.2 From the analysis, the meshing generated is shown in the figure below:- Loading condition and boundary Before the simulation can be run on the platform, it is important to note that the boundary conditions in the form of construction fixture are defined. The figure below shows the load and fixtures applied on the beam arm in the software:- The loading process and loading points are shown below:- The force magnitude calculated in the table below Load case Load ton Force (kN) 1 5 306.562 2 15 429.187 3 17.5 459.843 4 35 674.437 The moment of bending The calculation of bending moment of the analysis was done followed by stress and deflection with equations referring to the ANSI-NDS for the steel and wood construction which is applied to free body diagram. The calculation is given below: L= 23470mm = 23.47 m L / 2= 11735 mm = 11.74 m a= 9785 mm = 9.79 m b= 13685 mm = 13.69 m Where, L = effective length of girder (m) a = Distance of point of load (m) b = Distance of point of load (m) Wise bending moment calculation The bending moment is calculated in three different section as shown in the figure below The calculated values for the moment are shown in the table below:- Load case Section Distance Bending moment (KN m) 5 ton Section 1 0 < x < 9.79 1013.200 Section 2 0 < x < 13.69 1013.324 Section 3 0 < x < 23.47 0.457 15 ton Section 1 0 < x < 9.79 1313.219 Section 2 0 < x < 13.69 1313.295 Section 3 0 < x < 23.47 0.457 17.5 ton Section 1 0 < x < 9.79 1388.212 Section 2 0 < x < 13.69 1388.288 Section 3 0 < x < 23.47 0.458 35 ton Section 1 0 < x < 9.79 1913.162 Section 2 0 < x < 13.69 1913.238 Section 3 0 < x < 23.47 0.458 The calculation are as follows for the beam. As per the above table, the work load of 5 tons the normal stress is calculated as:- Ơmax = My/I = 1013324 x (775/1650535) = 47.58 MPa 2. The work load of 15 tons Ơmax = My/I = 1313295445 x (775/1650535) = 61.66 MPa 3. The work load of 17.5 tons Ơmax = My/I = 1388288296 x (775/1650535) = 65.19 MPa 4. The work load of 35 tons Ơmax = My/I = 1913238257 x (775/1650535) = 89.83 MPa Where: Ơmax = Maximum normal stress (MPa) M = bending moment (Nm) y = distance from neutral axis (mm) I = Moment of inertia xx (cm4) The normal stress simulation results The simulation results show that the normal stress induced in the member the resultant output is shown below:- The design optimization The obtained simulation results are according to the von Mises stress at the maximum loading condition are expected to be below stress as per AISC regulations under allowable stress design (ASD) criteria. It is known that the tensile strength of the construction material is 250 Mpa. The resultant maximum working stress limit is determined as follows: Ra≤ Rn/ Ω Ra≤ 250/ 1.67 Ra≤ 150 Where: Ra = Working or Design stress Limit, Rn = Maximum allowable stress of the material Ω = safety factor Results of von Mises stress simulation are shown in Figure 8a, 8b, 8c and 8d The design can be shown below Conclusion In the simulation of this model in Solidworks, it only requires loads and span initialization. The importance of these results is to help in cost reduction and improve beam stability. Optimal designs can be standardized by Finite Element Methods and hence commercialized for cost effectiveness. Work Cited Bhutta, Muhammad Mahmood Aslam, et al. "USING FINITE ELEMENT ANALYSIS FOR DESIGN OPTIMIZATION OF TWIN BEAM CRANE ARM." Science International 28.1 (2016). Chen, Xiaoguan, Timothy K. Hasselman, and Douglas J. Neill. "Reliability based structural design optimization for practical applications." Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. 1997. Gandomi, Amir Hossein, et al., eds. Metaheuristic applications in structures and infrastructures. Newnes, 2013. Yang, Xin-She, and Suash Deb. "Multiobjective cuckoo search for design optimization." Computers & Operations Research 40.6 (2013): 1616-1624. Yi, Sinan, Gengdong Cheng, and Liang Xu. "Stiffness design of heterogeneous periodic beam by topology optimization with integration of commercial software." Computers & Structures 172 (2016): 71-80. Read More