Question

Q.2 (a) (Continued) (11) For an isoparametric element, explain the relationship between shape functions, the geometry of the element and the shape the loaded element will deform to. (3 marks) (iv) Describe the relationship between structural equilibrium and the minimum potential energy state. (3 marks) (b) Imman F FIGURE Q2b: 3 Springs (0) Derive an expression for the Total Potential Energy of the structure shown above in Q2b. (5 marks) (1) Apply the minimum potential energy method to derive the governing equilibrium equations of the structure in terms of the joint displacements. (3 marks) (c) A vertical uniform bar of length L and uniform cross section A is held at one end. The bar has Young's Modulus E and density p. It is subject to gravity g in the vertical direction. It is modelled using a 3 node 10 bar element with the shape function [N]- 2x2x E Z 1-4x2xx + 2 1 Determine the consistent load vector for the element. (4 marks) (d) Describe the processing steps required to carry out a practical Finite Element Analysis of an engineering component using commercial software such as (6 marks) Total 30 Marks ANSYS.

Answer 1

sol)... from the above given data........

2a)iii)........The Isoparametric method lead to simple computer program formulation, and is generally applicable for two and three dimensional stress analysis and for non structural problems.

the Isoparametric formulation allow elements to created that are non rectangular and have curved sides.

For an element day 2-D Dinar briangular element the dis placement function define as V3 • U3 V2 I U2 (22, Yz) N3 0 N₂ su o pures Uz N3 Ni N₂ o V2 10 V3 [Nila ss where [neid - shape function matrin for defining des placement şsi Nodal " vector Similarly giomiby for tringle defined as - Hi Я 0 N3 212 Ni N₂ O 0 N2 N3 Ni 1932-1 313 Y
2a)iv)........

Structural equilibrium-

A structure is an equilibrium when all forces or moments acting on it must be balanced.

Or we can say that net force or net moment on the structure is necessary to be Zero than given structure is in equilibrium.

For an equilibrium structure each and every force is restricted by any other force to make it equilibrium.

So all vertical , horizontal , moment must to be Zero.

MINIMUM POTENTIAL ENERGY STATE--

As stability is inversely proportional to energy.

Higher the energy lower it's stability so for high stability energy must be lower .

It is a fundamental concepts of science it indicates that a low temperature at structure body shall deform or displace to a position that minimize the totals potential energy being converted into Kinetic energy.

2b)i).......

& 20 - Date BMW moramo a Total The element 1 is potential energy Ap for 2. 0) ТР 2 is = 1 Kg (U3-U,) - fix ,- fox V3 The potential energy Ap for element = Į K2 104 - Ug) ² - Fox Uz - fun Uy A (2) The 3 is e potential energy Ap for element Tp (3) = 1 kg (U₂-04) – fx 2 - fua Uy The total potential energy Ap for Spir Tp the system is ♡ Wil roce)
2b)ii)...........

2 - ( ) Date Minimizing the total potential energy tp. (4) Р. СО2 – ҚО3 +К,0 fit (3) Отр = 0 = kg, – кач - куч - ov, D. ъ л ОЛе — 0 — күз – Kira, K, Uу (2) duz tkz Ug - t (32) "3 2 л а) Juy — О = K, ич - К., 03 - кру GANT (2) (5) Чg fud
as per HomeworkLib rule i have solved four subparts..

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Answer 2

sol)... from the above given data........

2a)iii)........The Isoparametric method lead to simple computer program formulation, and is generally applicable for two and three dimensional stress analysis and for non structural problems.

the Isoparametric formulation allow elements to created that are non rectangular and have curved sides.

For an element day 2-D Dinar briangular element the dis placement function define as V3 • U3 V2 I U2 (22, Yz) N3 0 N₂ su o pures Uz N3 Ni N₂ o V2 10 V3 [Nila ss where [neid - shape function matrin for defining des placement şsi Nodal " vector Similarly giomiby for tringle defined as - Hi Я 0 N3 212 Ni N₂ O 0 N2 N3 Ni 1932-1 313 Y
2a)iv)........

Structural equilibrium-

A structure is an equilibrium when all forces or moments acting on it must be balanced.

Or we can say that net force or net moment on the structure is necessary to be Zero than given structure is in equilibrium.

For an equilibrium structure each and every force is restricted by any other force to make it equilibrium.

So all vertical , horizontal , moment must to be Zero.

MINIMUM POTENTIAL ENERGY STATE--

As stability is inversely proportional to energy.

Higher the energy lower it's stability so for high stability energy must be lower .

It is a fundamental concepts of science it indicates that a low temperature at structure body shall deform or displace to a position that minimize the totals potential energy being converted into Kinetic energy.

2b)i).......

& 20 - Date BMW moramo a Total The element 1 is potential energy Ap for 2. 0) ТР 2 is = 1 Kg (U3-U,) - fix ,- fox V3 The potential energy Ap for element = Į K2 104 - Ug) ² - Fox Uz - fun Uy A (2) The 3 is e potential energy Ap for element Tp (3) = 1 kg (U₂-04) – fx 2 - fua Uy The total potential energy Ap for Spir Tp the system is ♡ Wil roce)
2b)ii)...........

2 - ( ) Date Minimizing the total potential energy tp. (4) Р. СО2 – ҚО3 +К,0 fit (3) Отр = 0 = kg, – кач - куч - ov, D. ъ л ОЛе — 0 — күз – Kira, K, Uу (2) duz tkz Ug - t (32) "3 2 л а) Juy — О = K, ич - К., 03 - кру GANT (2) (5) Чg fud
as per HomeworkLib rule i have solved four subparts..

(Hope this answer helped you.Please like.Happy learning.)

Answer 3

sol)... from the above given data........

2a)iii)........The Isoparametric method lead to simple computer program formulation, and is generally applicable for two and three dimensional stress analysis and for non structural problems.

the Isoparametric formulation allow elements to created that are non rectangular and have curved sides.

For an element day 2-D Dinar briangular element the dis placement function define as V3 • U3 V2 I U2 (22, Yz) N3 0 N₂ su o pures Uz N3 Ni N₂ o V2 10 V3 [Nila ss where [neid - shape function matrin for defining des placement şsi Nodal " vector Similarly giomiby for tringle defined as - Hi Я 0 N3 212 Ni N₂ O 0 N2 N3 Ni 1932-1 313 Y
2a)iv)........

Structural equilibrium-

A structure is an equilibrium when all forces or moments acting on it must be balanced.

Or we can say that net force or net moment on the structure is necessary to be Zero than given structure is in equilibrium.

For an equilibrium structure each and every force is restricted by any other force to make it equilibrium.

So all vertical , horizontal , moment must to be Zero.

MINIMUM POTENTIAL ENERGY STATE--

As stability is inversely proportional to energy.

Higher the energy lower it's stability so for high stability energy must be lower .

It is a fundamental concepts of science it indicates that a low temperature at structure body shall deform or displace to a position that minimize the totals potential energy being converted into Kinetic energy.

2b)i).......

& 20 - Date BMW moramo a Total The element 1 is potential energy Ap for 2. 0) ТР 2 is = 1 Kg (U3-U,) - fix ,- fox V3 The potential energy Ap for element = Į K2 104 - Ug) ² - Fox Uz - fun Uy A (2) The 3 is e potential energy Ap for element Tp (3) = 1 kg (U₂-04) – fx 2 - fua Uy The total potential energy Ap for Spir Tp the system is ♡ Wil roce)
2b)ii)...........

2 - ( ) Date Minimizing the total potential energy tp. (4) Р. СО2 – ҚО3 +К,0 fit (3) Отр = 0 = kg, – кач - куч - ov, D. ъ л ОЛе — 0 — күз – Kira, K, Uу (2) duz tkz Ug - t (32) "3 2 л а) Juy — О = K, ич - К., 03 - кру GANT (2) (5) Чg fud
as per HomeworkLib rule i have solved four subparts..

(Hope this answer helped you.Please like.Happy learning.)