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Using Finite element method to show is Dar exist for f(x)-k! + 1. Support f: [-1, 1] →R
Show weak derivative Df does not exist for f(x) 1
Show weak derivative Df does not exist for f(x) 1
Show weak derivative Df does not exist for f(x) 1
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Elem...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
where Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.)...
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
PLEASE WRITE/PRINT CEARLY AND SOLVE USING THE FINITE ELEMENT METHOD WHICH INCLUDE MATRICIES 1. A wall...
PLEASE WRITE/PRINT CEARLY AND SOLVE USING THE FINITE ELEMENT
METHOD WHICH INCLUDE MATRICIES
1. A wall of an industrial oven consists of two different materials, as depicted in Figure. The first layer is composed of 5 cm of insulating cement with a clay binder that has a thermal conductivity of 0.08 W/m K. The second layer is made from 15 cm of 6-ply asbestos board with a thermal conductivity of 0.074 W/mK (W/m °C). The inside oven air is 400°C...
Q3 (Prove that P∞ k=1 1/kr < ∞ if r > 1) . Let f : (0,∞) → R be a twice differentiable function with f ''(x) ≥ 0 for all x ∈ (0,∞). (a) Show that f '(k) ≤ f(k + 1) − f(k) ≤ f '(...
Q3 (Prove that P∞ k=1 1/kr < ∞ if r > 1) . Let
f : (0,∞) → R be a twice differentiable function with f ''(x) ≥ 0
for all x ∈ (0,∞).
(a) Show that f '(k) ≤ f(k + 1) − f(k) ≤ f '(k + 1) for all k ∈
N.
(b) Use (a), show that Xn−1 k=1 f '(k) ≤ f(n) − f(1) ≤ Xn k=2 f
'(k).
(c) Let r > 1. By finding...
Question 3 (10 marks) A shaft is to be modelled by finite element method. Describe an appropriate...
Finite element method
Question 3 (10 marks) A shaft is to be modelled by finite element method. Describe an appropriate type of element that can be used to analyse the shaft. What is the minimum number of elements that must be used? Sketch the finite element model annotated with numbered nodes and numbered elements, and clearly show the degree of freedoms. Material: steel, Esteel | 3000 N 4.x=뉴94= 1.25x10% mm? 150 mm75 mm125 mm
Question 3 (10 marks) A shaft...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Determine the nodal displacements and find the reaction forces using the finite element method. Correct Answer:...
Determine the nodal displacements and find the reaction forces
using the finite element method.
Correct Answer:
1 m 1000 kN - Determine displacements and reactions E = 210 GPa 1 for 1 and 2 A=6x10-4 m| E = 210 GPa 1 m →X A=672x10-4 m2 for 3 d2x = 11.91x10-m; dăx = 5.613x10-'m . Fix =-500kN; F1, =-500kN; F2y = 0; F;, = 707 kN
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2...
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
Show weak derivative Df does not exist for f(x) 1
Show weak derivative Df does not exist for f(x) 1
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
Section 1: Finite Element Derivation and Validation In this section of the report you will develop your own Finite Element method for 1-dimensional axial loading. The governing equation for displacement, u is Poisson's Equation: อั1 where E is the modulus of elasticity, A(a) is the cross-sectional area as a function of length, and q(x) is the loading distribution as a function of length. The weak form of this equation with 0 1. Starting from the weak form of the governing...
where
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) < 00, then {x E X (z) > 0} is a countable set. (HINT: Show that for every k E N the set {x E X | f(x) > k-1} is finite.) f(x)-sup f(x) | F is any finite subset of X TEF
Problem 36. Assume f : X → [0, oo]. Prove that if Σ f(x) 0} is a countable set. (HINT: Show that...
PLEASE WRITE/PRINT CEARLY AND SOLVE USING THE FINITE ELEMENT
METHOD WHICH INCLUDE MATRICIES
1. A wall of an industrial oven consists of two different materials, as depicted in Figure. The first layer is composed of 5 cm of insulating cement with a clay binder that has a thermal conductivity of 0.08 W/m K. The second layer is made from 15 cm of 6-ply asbestos board with a thermal conductivity of 0.074 W/mK (W/m °C). The inside oven air is 400°C...
Q3 (Prove that P∞ k=1 1/kr < ∞ if r > 1) . Let
f : (0,∞) → R be a twice differentiable function with f ''(x) ≥ 0
for all x ∈ (0,∞).
(a) Show that f '(k) ≤ f(k + 1) − f(k) ≤ f '(k + 1) for all k ∈
N.
(b) Use (a), show that Xn−1 k=1 f '(k) ≤ f(n) − f(1) ≤ Xn k=2 f
'(k).
(c) Let r > 1. By finding...
Finite element method
Question 3 (10 marks) A shaft is to be modelled by finite element method. Describe an appropriate type of element that can be used to analyse the shaft. What is the minimum number of elements that must be used? Sketch the finite element model annotated with numbered nodes and numbered elements, and clearly show the degree of freedoms. Material: steel, Esteel | 3000 N 4.x=뉴94= 1.25x10% mm? 150 mm75 mm125 mm
Question 3 (10 marks) A shaft...
(40 pts) 2a. Show that u(z) is the solution to the problem where k(x)-1 for x < 1/2 and k = 2 for x > 1 /2. 2b. Set up the weak form for the differential equation above and the resulting element stiffness and element load vector and calculate the element stiffness matrix and load vector for 4 quadratic elements by using the Gaussian quadrature that is going to exactly calculate the integrals Then set up the global K and...
Determine the nodal displacements and find the reaction forces
using the finite element method.
Correct Answer:
1 m 1000 kN - Determine displacements and reactions E = 210 GPa 1 for 1 and 2 A=6x10-4 m| E = 210 GPa 1 m →X A=672x10-4 m2 for 3 d2x = 11.91x10-m; dăx = 5.613x10-'m . Fix =-500kN; F1, =-500kN; F2y = 0; F;, = 707 kN
Solve the two problems below using the finite element method with Euler-Bernoulli beam element. 2) Assume a simply supported beam of length 1 m subjected to a uniformly distributed load along its length of 100 N/cm. The modulus of elasticity is 207 GPa. The beam is of rectangular cross-section with a width equal to 0.01 m and a depth equal to 0.02 m. Using only one beam element, determine the deflection and maximum stress at midspan.
Solve the two problems...
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