SummaryOfFormulas

SummaryOfFormulas - Short summary of formulas in the course...

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Unformatted text preview: Short summary of formulas in the course TMHL03 Mechanics of Light Weight Structures 2 3D Linear Isotropic Static Elasticity Equilibrium Relations ∂σ x ∂x + ∂τ xy ∂y + ∂τ xz ∂z + b x = 0 (1) ∂τ xy ∂x + ∂σ y ∂y + ∂τ yz ∂z + b y = 0 (2) ∂τ xz ∂x + ∂τ yz ∂y + ∂σ z ∂z + b z = 0 (3) Kinematic Relations ε x = ∂u ∂x , ε y = ∂v ∂y , ε z = ∂w ∂z (4) γ xy = ∂u ∂y + ∂v ∂x (5) γ yz = ∂v ∂z + ∂w ∂y (6) γ xz = ∂u ∂z + ∂w ∂x (7) Constitutive Relations ε x = [ σ x- ν ( σ y + σ z )] /E (8) ε y = [ σ y- ν ( σ x + σ z )] /E (9) ε z = [ σ z- ν ( σ x + σ y )] /E (10) γ xy = τ xy /G, γ yz = τ yz /G, γ xz = τ xz /G (11) where the shear modulus G is G = E 2(1 + ν ) (12) Remarks: • Here we find 15 unknowns and 15 equations • These equations can easily be extended to include thermal effects 3 In-plane loaded Linear Isotropic Plates in Cartesian coordi- nates Equilibrium Relations ∂σ x ∂x + ∂τ xy ∂y + b x = 0 (13) ∂τ xy ∂x + ∂σ y ∂y + b y = 0 (14) (15) Kinematic Relations ε x = ∂u ∂x , ε y = ∂v ∂y (16) γ xy = ∂u ∂y + ∂v ∂x (17) Constitutive Relations - Plane Stress Conditions...
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SummaryOfFormulas - Short summary of formulas in the course...

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