New masters of poster design volume 2 part 1

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... 307Chapter 6. Plates: out -of- plane motion 311 6 .1. Kirchhoff–Love hypotheses 3 12 6 .1. 1. Local displacements 3 12 6 .1 .2. Local and global strains 313 6 .1 .2. 1. Local strains 313 6 .1 .2. 2. Global flexure ... motion 25 95 .1. Introduction 26 05 .1. 1. Plate geometry 26 05 .1 .2. Incidence of plate geometry on the mechanicalresponse 26 05 .2. Kirchhoff–Love model 26 25 .2. 1. Love simplifications 26 25 .2. 2. Degrees ... equations of vibration 4078 .1. 5 .2. Natural modes of vibration of a circular ring 410 8 .2. Thin shells 4 12 8 .2. 1. Local and global tensor of small strains 4 12 8 .2. 1. 1. Local displacement field 4 12 8 .2. 1 .2. ...

... ⎭⎬⎫⎩⎨⎧+⎭⎬⎫⎩⎨⎧ΔΔ=⎭⎬⎫⎩⎨⎧ΔΔ⎥⎦⎤⎢⎣⎡ 2 1 2 1 )1( 2 1 )0( 22 21 12 1 1 RRFFUUKKKK (2. 21) Solving the Eq. (2. 21) , we can obtain: {}[]{}{}[]{}() 22 11 1 1 111 UKRFKU Δ−+Δ=Δ− (2. 22) {}[]{}[]{}{} 21 12 2 222 RUKUKF ... ⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧ΔΔΔ=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧ΔΔ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡ukkuFFFUUKKKKKKKKKλ033 323 1 23 222 1 13 12 1 1 (2. 1) And rewriting again FFFUUKKKKkkkuΔ⎭⎬⎫⎩⎨⎧=⎭⎬⎫⎩⎨⎧ΔΔ=⎭⎬⎫⎩⎨⎧ΔΔ⎥⎦⎤⎢⎣⎡ 1 22 21 12 1 1 λλ (2. 2) To solve Eq. (2. 2) by using ... ⎭⎬⎫⎩⎨⎧ΔΔ=⎭⎬⎫⎩⎨⎧ΔΔ⎥⎦⎤⎢⎣⎡ 2 1 2 1 22 21 12 1 1 FFUUKKKK (2. 6) where K 11 and K 22 are the stiffness matrices of free nodes and fixed nodes, respectively; K 12 and K 21 are resulted stiffness...