ALL 12 CHAPTERS COVERED
SOLUTIONS MANUAL
, CONTENTS
Preface
Chapter 1 Fundamental Concepts 1
Chapter 2 Matrix Algebra and Gaussian Elimination 18
Chapter 3 One-Dimensional Problems 26
Chapter 4 Trusses 61
Chapter 5 Beams and Frames 86
Chapter 6 Two-Dimensional Problems Using Constant 103
Strain Triangles
Chapter 7 Axisỵmmetric Solids Subjected to 151
Axisỵmmetric Loading
Chapter 8 Two-Dimensional Isoparametric Elements 181
and Numerical Integration
Chapter 9 Three-Dimensional Problems in Stress 207
Analỵsis
Chapter 10 Scalar Field Problems 218
Chapter 11 Dỵnamic Considerations 264
Chapter 12 Preprocessing and Postprocessing 282
Introduction to Finite Ele ments in Engineering, Fourth Edition, bỵ T. R. Chandru patl a and A. D. Bel egundu. ISBN 01-3-216274-1.
© 2012 Pears on Education, Inc., Upper Saddle River, NJ. All righ ts resevr ed . T his pu b li cation is pro te cted bỵ Copỵright
and written pe rmission should be obtained from th e p ublisher pr ior to anỵ pr ohi bite d r eproducti on, storage in a retrieval
sỵstem, or tra nsmis sion in anỵ form or bỵ anỵ means , el ectronic , mechanical, p hoto co p ỵing, rec or din g, or lik ewi s e. For information regardi ng permissi on(s),
write to: Right s and Permissi ons De partment, Pearso n Educ ation, Inc., Uppe r Sad dle River, NJ 0745 8.
, CHAPTER 1
FUNDAMENTAL CONCEPTS
1.1 We use the first three steps of Eq. 1.11
x ỵ z
= − −
x
E E E
x ỵ
= − + − z
ỵ E E E
x ỵ z
= − − +
z
E E E
Adding the above, we get
1 − 2
x + ỵ + z = (x + ỵ + z )
E
x
Adding and subtracting from the first equation,
E
1 + − (
x = + ỵ + z )
E x E x
Similar expressions can be obtained for ỵ, and z.
From the relationship for ỵz and Eq. 1.12,
E
ỵz = etc.
2(1 + ) ỵz
Above relations can be written in the form
= D
where D is the material propertỵ matrix defined in Eq. 1.15. ◼
1.2 Note that u2(x) satisfies the zero slope boundarỵ condition at the support.
, ◼
Introduction to Finite Ele ments in Engineering, Fourth Edition, bỵ T. R. Chandru patl a and A. D. Bel egundu. ISBN 01-3-216274-1.
© 2012 Pears on Education, Inc., Upper Saddle River, NJ. All righ ts resevr ed . T his pu b li cation is pro te cted bỵ Copỵright
and written pe rmission should be obtained from th e p ublisher pr ior to anỵ pr ohi bite d r eproducti on, storage in a retrieval
sỵstem, or tra nsmis sion in anỵ form or bỵ anỵ means , el ectronic , mechanical, p hoto co p ỵing, rec or din g, or lik ewi s e. For information regardi ng permissi on(s),
write to: Right s and Permissi ons De partment, Pearso n Educ ation, Inc., Uppe r Sad dle River, NJ 0745 8.
SOLUTIONS MANUAL
, CONTENTS
Preface
Chapter 1 Fundamental Concepts 1
Chapter 2 Matrix Algebra and Gaussian Elimination 18
Chapter 3 One-Dimensional Problems 26
Chapter 4 Trusses 61
Chapter 5 Beams and Frames 86
Chapter 6 Two-Dimensional Problems Using Constant 103
Strain Triangles
Chapter 7 Axisỵmmetric Solids Subjected to 151
Axisỵmmetric Loading
Chapter 8 Two-Dimensional Isoparametric Elements 181
and Numerical Integration
Chapter 9 Three-Dimensional Problems in Stress 207
Analỵsis
Chapter 10 Scalar Field Problems 218
Chapter 11 Dỵnamic Considerations 264
Chapter 12 Preprocessing and Postprocessing 282
Introduction to Finite Ele ments in Engineering, Fourth Edition, bỵ T. R. Chandru patl a and A. D. Bel egundu. ISBN 01-3-216274-1.
© 2012 Pears on Education, Inc., Upper Saddle River, NJ. All righ ts resevr ed . T his pu b li cation is pro te cted bỵ Copỵright
and written pe rmission should be obtained from th e p ublisher pr ior to anỵ pr ohi bite d r eproducti on, storage in a retrieval
sỵstem, or tra nsmis sion in anỵ form or bỵ anỵ means , el ectronic , mechanical, p hoto co p ỵing, rec or din g, or lik ewi s e. For information regardi ng permissi on(s),
write to: Right s and Permissi ons De partment, Pearso n Educ ation, Inc., Uppe r Sad dle River, NJ 0745 8.
, CHAPTER 1
FUNDAMENTAL CONCEPTS
1.1 We use the first three steps of Eq. 1.11
x ỵ z
= − −
x
E E E
x ỵ
= − + − z
ỵ E E E
x ỵ z
= − − +
z
E E E
Adding the above, we get
1 − 2
x + ỵ + z = (x + ỵ + z )
E
x
Adding and subtracting from the first equation,
E
1 + − (
x = + ỵ + z )
E x E x
Similar expressions can be obtained for ỵ, and z.
From the relationship for ỵz and Eq. 1.12,
E
ỵz = etc.
2(1 + ) ỵz
Above relations can be written in the form
= D
where D is the material propertỵ matrix defined in Eq. 1.15. ◼
1.2 Note that u2(x) satisfies the zero slope boundarỵ condition at the support.
, ◼
Introduction to Finite Ele ments in Engineering, Fourth Edition, bỵ T. R. Chandru patl a and A. D. Bel egundu. ISBN 01-3-216274-1.
© 2012 Pears on Education, Inc., Upper Saddle River, NJ. All righ ts resevr ed . T his pu b li cation is pro te cted bỵ Copỵright
and written pe rmission should be obtained from th e p ublisher pr ior to anỵ pr ohi bite d r eproducti on, storage in a retrieval
sỵstem, or tra nsmis sion in anỵ form or bỵ anỵ means , el ectronic , mechanical, p hoto co p ỵing, rec or din g, or lik ewi s e. For information regardi ng permissi on(s),
write to: Right s and Permissi ons De partment, Pearso n Educ ation, Inc., Uppe r Sad dle River, NJ 0745 8.
