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. Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25?
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. Calculate the element stiffness matrix for the axisymmetric triangul...
Calculation of Element Stiffness Matrix for Axisymmetric Triangular Element
Given Parameters:
- α = 10 x 10-6/°C
- E = 2 x 105 N/mm2
- ν = 0.25
- Temperature increase = 15°C
Element Geometry:
Element Stiffness Matrix:
The element stiffness matrix for the axisymmetric triangular element can be calculated using the following equation:
where:
- kij = element stiffness matrix
- E = modulus of elasticity
- ν = Poisson's ratio
- α = coefficient of thermal expansion
- t = element thickness
- A = element area
- Bi and Bj = strain-displacement matrix
- D = stress-strain matrix
Calculation Steps:
- Calculate the element area (A) using the coordinates of the nodes.
- Calculate the element thickness (t) based on the given geometry.
- Calculate the strain-displacement matrix (B) using the following equation:
- Calculate the stress-strain matrix (D) using the following equation:
- Calculate the element stiffness matrix (k) using the equation mentioned above.
- Apply the temperature increase to the element stiffness matrix using the following equation:
- The final element stiffness matrix is obtained after applying the temperature increase.
Result:
The element stiffness matrix for the axisymmetric triangular element after applying the 15°C temperature increase is obtained using the above calculation steps.
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. Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25?
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. Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about . Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25?.
. Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about . Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25?.
Solutions for . Calculate the element stiffness matrix for the axisymmetric triangular element shown in figure. The element experiences a 15o C increase in temperature. The co ordinates are in mm. Take α = 10 x10-6 / o C, E = 2 x 105 N/mm2 , ν = 0.25? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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