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Typical Length Scales in Biology IA lO microtubule DNA width width typical animal cell length of DNA in a chromosome
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Molecular Cellular Tissue Biomechanics Patrick Doyle(ChemE), Roger Kamm ME Be) Maxine Jonas(BE Goal: Develop a fundamental understanding of biomechanics over a wide range of length scales
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properties of finite dement soltions Noded point equilibrio At a node, the sow of he elemeat nodal forces s in equilibriun with Hhe externed loads
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How many quadrature points do you need to integrate a polynomial of order p= 3 exactly using Gauss'method
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Concept Question How many quadrature points do you need to integrate exactly the stiffness matrix of a lD finite element with quadratic interpolation for the displacements? gauss
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The finite element method(I for three-diwnensional robles Potential enery applied to one eleet
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cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates
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Numerical integration Consider He 4-D integral =+(s 1 Seek n-point apploxiwisfions G~2M =1 are the weights and
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How many zero eigenvalues do you think any element stiffness matrix (regardless of the type of finite element nterpolation should have in 2D and 3D, respectively?
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Finite element wodel of a beam(Euler-Bernollia- governing eQuations
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