Engineering Analysis of Smart Material Systems by Donald J. Leo

By Donald J. Leo

The publication offers a pedagogical method that emphasizes the actual strategies of energetic fabrics and the layout and regulate of engineering systems.  it is going to even be a reference textual content for training engineers who may well comprehend the fundamental rules of energetic fabrics yet be interested in studying extra approximately particular applications.  The textual content features a variety of labored examples, layout difficulties, and homework difficulties (with a strategies handbook) that might be helpful for either teachers and practising engineers.

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83) in a Cartesian coordinate system defined in the 1, 2, and 3 directions results in the expressions dU = ( f 1 xˆ1 + f 2 xˆ2 + f 3 xˆ3 ) · (du 1 xˆ1 + du 2 xˆ2 + du 3 xˆ3 ) = f 1 du 1 + f 2 du 2 + f 3 du 3 . 84) The energy function U is a function of the displacement coordinates u i ; therefore, we can express the total differential of the function U as dU = ∂U ∂U ∂U du 1 + du 2 + du 3 . 85), we see that f1 = ∂U ∂u 1 f2 = ∂U ∂u 2 f3 = ∂U . 86) is an important relationship between the energy function and the forces that act on a system.

In Chapter 5 we focus on the basic properties of piezoelectric ch01 JWPR009-LEO 18 July 19, 2007 19:37 INTRODUCTION TO SMART MATERIAL SYSTEMS materials incorporated into beam and plate elements. Beams and plates are used to examine the properties of distributed spatial sensing and actuation using piezoelectric materials. Shape memory alloys is the second set of materials studied in this book. In Chapter 6 we focus on the development of constitutive models for shape memory alloys and their use in understanding mechanical response as a function of temperature.

9) T3 = T31 xˆ1 + T32 xˆ2 + T33 xˆ3 , where Ti j is the component of stress vector T i with a component in the j direction. This analysis demonstrates that the state of a solid element is defined by nine strain components, Si j , and nine stress components, Ti j . 10) and this symmetry reduces the number of independent stress and strain components from nine to six. 11):  S11  S   22     S33  . 12) 2S12 The stress and strain vectors are also written in compact, or Voigt, notation through the following definitions: S1 = S11 T1 = T11 S2 = S22 T2 = T22 S3 = S33 T3 = T33 S4 = S23 + S32 = 2S23 T4 = T23 = T32 S5 = S31 + S13 = 2S13 T5 = T31 = T13 S6 = S12 + S21 = 2S12 T6 = T12 = T21 .

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