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A computational method called finite element analysis (FEA) predicts how an object will react to physical forces, vibrations, heat, fluid flow, and other influences. Finite element analysis determines whether a product will break, work as intended, or both. When writing finite element analysis homework, most students encounter several problems that make completing homework quite tedious. As a result, students search online, "Can someone do my finite element analysis homework?" TutorBin offers the best help with finite element analysis homework as a consequence.

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**Structural analysis**: There are both linear and nonlinear models in it. The linear models presume that the material is not deformed and employ basic parameters. The nonlinear models put the material under stress beyond its elastic limits. The amount of stress directly relates to the quantity of deformation produced.

**The vibration analysis** finds application in evaluating materials for resistance to vibration, shock, and impact. These occurrences also affect the material's vibration frequency, which results in resonance and subsequent breakdown.

**Fatigue analysis**: It investigates different impacts of cyclic loadings on the structure or material, and the study forecasts how long the material will last. The failure brought on by fatigue demonstrates the material's resistance to damage. The study displays the likely locations for fracture propagation.

**Heat transfer analysis**: A study analyses the conductivity or the thermal fluid dynamics of the structure or material, consisting of steady-state or transient transfer.

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**Q1:**(20%) Use (a) the Galerkin’s method and (b) Minimum Potential approach to find the displacement at the midpoint of the rode shown under the body force g. \text { Consider } u=a_{1}+a_{2} x+a_{3} x^{2} See Answer**Q2:**2 (15%) Consider a tapered bar of circular cross section. The length of the bar is 1m, and the radius varies as r(x)= 0.05–0.04x, where r and x are in meters. Assume Young's modulus E = 100 MPa. Both ends of the bar are fixed and F = 10,000 N is applied at the center. Determine the displacements, axial force distribution and the wall reactions using four elements of equal length. See Answer**Q3:**The vertical column shown in the picture has both endsfixed. The elastic modulus E is uniform. Its cross-sectional area A(x) is uniform in the upper part and varieslinearly in the lower part. It carries its own weight, so thatthe load is proportional to the cross-sectional area: See Answer**Q4:**5 (20%) A traction Tx = 10 kN/m is applied at the top of the plane problem shown, with the bottom side is fixed and the top side is only allowed to move horizontally. E = 10GPAand v = 0.25. Use one plane element to calculate the stress and strain components for the case of (a) thickness t = 0.1 m and (b) thickness t = 10 m. See Answer**Q5:**.4 (15%) Find the heat transfer per unit area through the composite wall in the figure.Assume one-dimensional heat flow and there is no heat flow between B and C. The thermal conductivities are ka = 0.04 W/(m-°C), ka = 0.1 W/ W/(m-°C), kc= 0.03 W/(m-°C), and kp = 0.06 W/(m-°C). See Answer**Q6:**.6 (15%) Calculate the shape function matrix [N] and strain-displacement matrix [B] of the cs telement shown in the figure See Answer**Q7:**The given framework (see Fig. 2) is loaded vertically by a force F = 5 kN. =The material parameters and dimensions are included E = 210000 MPa, A/= 0.5 m100 mm², a) Make a table with the node numbers and coordinates, and a table with the element numbers and the associated node connectivity. b) What are the element stiffness matrices of elements 3, 4, 7 and 8? To do this, first note the general form of the element stiffness matrix for rotated members as a support and then insert thecorresponding values. c) What is the vertical displacement of node vi? d) What stresses and strains do bars 2 and 13 experience?See Answer**Q8:**Q2. (10 points) The nodal coordinates of the triangular element are shown below. At the interior point P, the Y coordinate is 2.7 and N₂ = 0.4. Determine N₁, N3 at point P. Then determine the X coordinate at point P. Nodal coordinates are from nodes 1 to 3: (5,1) (2,6) (-2,-2)See Answer**Q9:**6.13-1 Assume that the patch test is passed for the mesh in Fig. 6.13-1a. If all nine nodes : are assigned displacements consistent with a field of constant strain, what loads at the internal node should result from the calculation [K]{D], and why?See Answer**Q10:**Textbook problem 6.3-6,page 249,ONLY parts (b&c).(10 points)Calculate the percentage error ngwhere uis the value ofthe integral You can do1eracreither/both the numerical and/or the analytical integrals using hand-cales or matlab.See Answer**Q11:**Consider a 4 node rectangular finite element given earlier in the class notes with x dimension a=3 cm and y dimension b-4 cm, and a thickness of 1 cm. For steel which has a mass density of 8 g/cm³, find the first row of the consistent mass matrix (8 terms) for the element and the first diagonal entry of the lumped mass matrix using the row-sum technique.See Answer**Q12:**1. Find the analytical solution for the following tapered beam under an axial load, solving for total deflection 8. The initial diameter di = 0.75 in, the final diameter df = 0.125 in, the length L = 12 in, Young's Modulus E = 29(10)6 psi and the force F = 178 kips. Derive using real numbers and procedure in class. *Can use calculator for definite integral step. 2. Use numerical methods to solve for total deflection with 1, 2, 3 and 4 elements. Do calculations by hand and show all work! May treat as springs in series. Graph deflection vs. number of elements to show convergence on analytical solution. d. 14 F LL 7See Answer**Q13:**For the beam below with fixed-fixed boundary conditions, do the following calculations by hand. Let k₁ = 480 #/in, k₂ = 310 #/in, k3 = 70 #/in, k4 = 90 #/in, k5 = 10 #/in, F₂ = 200 # and F3 = 500 #. 1. Solve for the displacements at nodes 1 through 4 (U₁, U₂, U3, and 4). 2. Solve for the reaction forces at both ends (R₁ and R4). R 1 F 2 TR ка www 42 3 K3 k 3 4. 4 3 mm K5 www 43 R 4See Answer**Q14:**For the tapered aluminum beam below experiencing pure conduction heat transfer with k = 221 W/mK, d₁ = 30 cm, d₁0= 12 cm, L = 9 m, T₁ = 70°C, and T₁0 = 10°C. The beam is solid round tapered with diameter as a function of position d(x). There are 10 nodes on the beam equally spaced. Note: Cannot factor out A for global thermal matrix since it is constantly changing. Use average area for element (A₁ +Ai+1/2). 1. Calculate the temperature for nodes 1-10 [°C]. 2. Plot T vs. x. 3. Calculate the total heat transfer rate q [W]. Calculations: Matlab or Excel will be accepted but you must show all work and describe what the code does. If working in groups you still need to show that you did the work on your own! 0 T. 10 -ød(x) +See Answer**Q15:**Please show all work Consider the continuously tapered beam under an axial load shown below. The initial diameter d₁ = 0.75 in, the final diameter df = 0.125 in, the length L = 12 in, Young's Modulus E = 29(10)6 psi and the force F = 178 kips. a. Use minimum total potential energy formulation to solve for total deflection & using 4 equally divided elements. b. Compare solution to analytical result. Note: Can use the derived formula from class. 1 d FSee Answer**Q16:**1. Find the analytical solution for the following tapered beam under an axial load, solving for total deflection 8. The initial diameter di = 0.75 in, the final diameter df = 0.125 in, the length L = 12 in, Young's Modulus E = 29(10)6 psi and the force F = 178 kips. Derive using real numbers and procedure in class. *Can use calculator for definite integral step.See Answer**Q17:**Please show all work Consider the continuously tapered beam under an axial load shown below. The initial diameter d₁ = 0.75 in, the final diameter df = 0.125 in, the length L = 12 in, Young's Modulus E = 29(10)6 psi and the force F = 178 kips. a. Use minimum total potential energy formulation to solve for total deflection 8 using 4 equally divided elements. b. Compare solution to analytical result. Note: Can use the derived formula from class. To LSee Answer**Q18:**For the tapered aluminum beam below experiencing pure conduction heat transfer with k = 221 W/mK, d₁ = 30 cm, d₁0= 12 cm, L = 9 m, T₁ = 70°C, and T₁0 = 10°C. The beam is solid round tapered with diameter as a function of position d(x). There are 10 nodes on the beam equally spaced. Note: Cannot factor out A for global thermal matrix since it is constantly changing. Use average area for element (A; +Ai+1/2). 1. Calculate the temperature for nodes 1-10 [°C]. 2. Plot T vs. x. 3. Calculate the total heat transfer rate q [W]. Calculations: Matlab or Excel will be accepted but you must show all work and describe what the code does. If working in groups you still need to show that you did the work on your own! 9 0 10 d; 10 -ød(x) +See Answer**Q19:**Please show all work Consider the continuously tapered beam under an axial load shown below. The initial diameter d₁ = 0.75 in, the final diameter df = 0.125 in, the length L = 12 in, Young's Modulus E = 29(10)6 psi and the force F = 178 kips. a. Use minimum total potential energy formulation to solve for total deflection 8 using 4 equally divided elements. b. Compare solution to analytical result. Note: Can use the derived formula from class. To LSee Answer**Q20:**Perform finite element analysis using SolidWorks Simulation on the attached file: Anchor Bracket 2-3.SLDPRT. Show the Von Mises stress as demonstrated in class. Note: split lines for hole are not necessary 30* the nowe pr right). Assume the following. • Material: • Mesh: . Fixture: . inum Fo Apply a Fixed (immovable) restraint on the inclined surface. External Load: 8600 N in the X-direction applied on the right, inside surface of the 16 mm diameter hole between user defined Split Lines. Determine the following: a. Use classical equations to compute stress at the inside (concave) surface and the outside (convex) surface of the anchor bracket at section B-B. Section B-B passes through the center of curvature of the curved beam and is considered to be a vertical line. Include a labeled free body diagram of the portion of the anchor bracket to the right of section B-B (show magnitude and direction of all reactions). b. Include a zoomed-in image of the hole so that the force Fx = 8600 N can clearly be seen to act between user specified Split Lines. c. Create a stress contour plot of von Mises stress in the anchor bracket. Include automatic labeling of maximum and minimum stress on this plot. 60 AISI 1010 Steel, hot rolled bar (use SI units) B In the Mesh property manager, select O Standard mesh; use the default mesh size. R40 I B 20 7 R100 30 पर 20 150 016 Surface is attached to a rigid frame (fixed).See Answer

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