1. Starting from the weak form of the governing equation, using the Galerkin method with two elements, with boundary conditions u(0)0 and u(L 0, and without specified external loads, derive a solution in the form: KHU where K is the stiffness matrix, U is the global displacement vector and Q is the global load vector. Use linear basis functions in your derivation and assume that the area is constant across each element. Be concise in the presentation of your working (use phrases like "col- lecting terms", and "similarly, the next integral is ..." to reduce the lines of working in your report). (15%)
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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 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...
need to solve the mathematical model to prove that we can get the equations i Q1...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
Answer #1 EM 4123/6123: Introduction to Finite Element Methods: Assignment 2 Assigned: Jan. 23, 2019, Due:...
Answer #1
EM 4123/6123: Introduction to Finite Element Methods: Assignment 2 Assigned: Jan. 23, 2019, Due: Jan 30, 2019, 11.00am 20 Points per problem. Total: 60 Points Derive the weak form of the variational statement for each of the following boundary value problems NOTE: Show all steps of derivation NOTE: Identify the conditions on the variation that are consistent with the specified boundary con- ditions. (Hint: the variation cannot be arbitrary where the value of solution is specified) 1. Poisson's...
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is...
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is sine cose 0 0 0 0 0 sine 0 0 0 -sine cose 0 0 In the previous section, we developed the stines matributed to bending for a beancement. This matracounts for lateral deplacements and rotaties teach mode andis TO 0 0 0 60-126 0 0 0 0 0 LO 621041 To represent the contribution of each term to nodal degrees of freedom, the...
need to solve the mathematical model to prove that we can get the equations i Q1...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
QI. A vertical pile is used to transfer the vertical load from the soft ground surface to the rock surface. It is assumed that the stiffness of the rock is sufficient to prevent any vertical displacement so that the lower edge of the rod may be considered as fixed. The soft ground acts on the pile along its length with a force...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
e. 18 Test Your Knowledge MULTIPLE CHOICE: Choose the one best answer. 1. Each element has...
e. 18 Test Your Knowledge MULTIPLE CHOICE: Choose the one best answer. 1. Each element has its own characteristic atom in which a. the atomic mass is constant. b. the atomic number is constant. c. the mass number is constant. d. Two of the above are correct. e. All of the above are correct. 2. Which of the following is not a trace element in the human body? a. iodine b. zinc c. iron d. calcium e. fluorine 3. A...
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...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
please use only the weighted resedual and gerkins
methods to prove it
1. A metal bar of length, L = 100 mm, and a constant cross-sectional area of A = 10 mm? is shown in figure Q1. The bar material has an elastic modulus, E = 200,000 N/mm2 with an applied load P at one end. The governing equation for elastostatic problems...
Q1 An elastic cantilever beam of varying cross section, as shown in Figure Q1(a), is subjected to an increase in temperature of 60°C in an unnatural environment. The equation governing the displacement of the elastic column and the finite element stiffness matrix are respectively given as -O and ΑΕ) - where A is the cross sectional area of the beam, E is the Young's modulus of the beam material, u is the displacement and / is the finite element length....
Answer #1
EM 4123/6123: Introduction to Finite Element Methods: Assignment 2 Assigned: Jan. 23, 2019, Due: Jan 30, 2019, 11.00am 20 Points per problem. Total: 60 Points Derive the weak form of the variational statement for each of the following boundary value problems NOTE: Show all steps of derivation NOTE: Identify the conditions on the variation that are consistent with the specified boundary con- ditions. (Hint: the variation cannot be arbitrary where the value of solution is specified) 1. Poisson's...
Section 4.4 Finite Element Formulation of Frames 235 256 of 929 where the transformation matrix is sine cose 0 0 0 0 0 sine 0 0 0 -sine cose 0 0 In the previous section, we developed the stines matributed to bending for a beancement. This matracounts for lateral deplacements and rotaties teach mode andis TO 0 0 0 60-126 0 0 0 0 0 LO 621041 To represent the contribution of each term to nodal degrees of freedom, the...
need to solve the mathematical model to prove
that we can get the equations i Q1 a methematically
QI. A vertical pile is used to transfer the vertical load from the soft ground surface to the rock surface. It is assumed that the stiffness of the rock is sufficient to prevent any vertical displacement so that the lower edge of the rod may be considered as fixed. The soft ground acts on the pile along its length with a force...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
e. 18 Test Your Knowledge MULTIPLE CHOICE: Choose the one best answer. 1. Each element has its own characteristic atom in which a. the atomic mass is constant. b. the atomic number is constant. c. the mass number is constant. d. Two of the above are correct. e. All of the above are correct. 2. Which of the following is not a trace element in the human body? a. iodine b. zinc c. iron d. calcium e. fluorine 3. A...
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