Recent content by chowdhury

Is there a good rubric on how to choose the order of polynomial basis in an Finite element method, let's say generic FEM, and the order of the differential equation? For example, I have the following equation to be solved ## \frac{\partial }{\partial x} \left ( \epsilon \frac{\partial u_{x}...

I have a voltage distribution ##V(x,y) = V_{dc}(x,y)+ V_{ac}(x,y) \cos(\omega t)##, I have derived the Matrix e. But I do not know how to extract it from the voltage, meaning I do not know how to find ##E_{x0} , E_{y0}, \delta E_{x}, \delta E_{y}## in terms of ##V_{dc}(x,y), V_{ac}(x,y)##...

Does anybody know how to derivemy above three queries? Thanks.

In this particular equation, I expect the result to be of rank ZERO. $$\nabla \cdot (\bf{\epsilon}^{S} \cdot \nabla \phi) = \nabla \cdot (\bf{e} : \nabla_{s} \bf{u}) = \textup{rank zero} $$

I understand up to this, I cannot say further below.

@anuttarasammyak : I am sorry, I am not clear how to proceed, better, I would seek @Orodruin as the Judge!

@anuttarasammyak : yes in most cases, Query 1.) here is what I try to follow $$\nabla \cdot (\bf{\epsilon}^{S} \cdot \nabla \phi) = \nabla \cdot (\bf{e} : \nabla_{s} \bf{u}) $$ Now $$\nabla_{i} \epsilon_{ij}^{S} \nabla_{j} \phi = \nabla_{i} \epsilon_{ij}^{S} \phi_{,j} =...

## \nabla ## is the usual operator in maths ##\nabla_s## is the symmetric part of the gradient operator, which results in strain of the material ##e## is the piezoelectric coefficient and it is a third rank tensor ##u## is a vector in space, so 3x1 vector. FYI, I copy the definitions from the...

@anuttarasammyak : I will provide after the last #16 of mine. Thanks for being so patient.

@Orodruin: @anuttarasammyak: I derived this quantity, following the book Acoustic Fields and Waves in Solids. Volume I Hardcover – April 20, 1973 $$ \bf{c^{eff}} = \bf{c^{E}} + e^{transpose} \cdot (\bf{(\epsilon^{S}})^{-1} \bf{e})$$ The notation my be incorrect, but the true nature is CORRECT...

@Orodruin : I was told this book is the Bible, and there is no mistake in it. Without complaining, which is easy to rant to anybody in the world, I took an introspective view and try to educate myself.

I applied the defintions, but could not find the reasonable notation, that is the problem.

@Orodruin : I have noticed that in the field of piezoelectricity, "they" denote like this, Here is another book, https://www.amazon.com/dp/3540686800/?tag=pfamazon01-20 What is driving me crazy is this statement, from the end of this book Acoustic Fields and Waves in Solids. Volume I...

@anuttarasammyak Here is the notation for double dot in the book,

@Orodruin : I understand the transpose operator appears in matrix operations, however, I have seen the transpose operation in a 3rd rank tensor in Wikipedia, as suggested by one of the moderators, @andrewkirk. What I am lacking how to represent them. Thanks for your clarification. How to say...