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ProblemsClear skill: Stress Balance Build a practice set

ProblemCourse & topicStatus

CONT:9910051An incompressible isotropic rubber is modeled as Mooney–Rivlin, with stored energy per unit reference volume…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910052A compressible isotropic solid has the neo-Hookean stored energy per unit reference volume…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910053Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910054Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910055Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910056A homogeneous deformation gradient, referred to coincident orthonormal bases, is…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910057The same F and Q as in Problem 57 are used.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910058At a spatial point the velocity gradient in a laboratory frame is…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910059Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910060A homogeneous isotropic Monel 400 coupon has Young’s modulus E = 179 GPa and Poisson’s ratio ν = 0.32.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910061A long AZ61A magnesium extrusion is isotropic and linearly elastic with E = 45.0 GPa and ν = 0.35.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910062A jacketed 4140 steel column occupies 0 ≤ x ≤ 55.0 mm, 0 ≤ y ≤ 40.0 mm, and 0 ≤ z ≤ H with H = 180 mm.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910063A homogeneous isotropic 316 stainless cube occupies 0 ≤ x, y, z ≤ L with L = 60.0 mm, E = 193 GPa, and ν = 0.30.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910064A solid circular phosphor-bronze shaft of radius R = 19.0 mm and length L = 920 mm is homogeneous, isotropic, and…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910065A compound circular shaft of length L = 740 mm is formed by a solid 6063-T5 aluminum core of radius a = 12.0 mm…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910066A rectangular 7050-T7451 aluminum bar occupies 0 ≤ x ≤ L, |y| ≤ c, |z| ≤ t/2, with L = 420 mm, c = 14.0 mm, and t…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910067A long thick-walled Ti-6Al-4V cylinder has inner radius a = 28.0 mm, outer radius b = 51.0 mm, E = 114 GPa, and ν…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910068An unbounded homogeneous isotropic solid has E = 110 GPa and ν = 0.33.

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910069A homogeneous isotropic C36000 brass rectangular block occupies 0 ≤ x ≤ 90.0 mm, 0 ≤ y ≤ 55.0 mm, and 0 ≤ z ≤ 40.0…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910070Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910071An incompressible isotropic tensile specimen obeys the Mooney–Rivlin stored energy per unit reference volume…

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910072Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910073Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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CONT:9910074Mathematical problem title

Stress BalanceContinuum Mechanics Problem Solving

Stress measures and local balance lawsContinuum Mechanics · Calculation

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An incompressible Mooney–Rivlin solid has

C_{10}=118\,\mathrm{kPa}

and

C_{01}=29.5\,\mathrm{kPa}

, with…

A thin circular disk of isotropic 70-30 cartridge brass is in plane stress

(\sigma_{33}=\sigma_{13}=\sigma_{23}=0)

…

An isotropic Cu–Be coupon has linearized moduli

E=128\,\mathrm{GPa}

and

\nu=0.30

and a linear thermal expansion…

An incompressible neo-Hookean continuum with

\sigma=-pI+\mu

B,

\mu=195\,\mathrm{kPa}

, and

B=FF^{\mathrm{T}}

…

An incompressible neo-Hookean block occupies the reference rectangular region

0\le

X_1\le

36.0\,\mathrm{mm}

,

0\le

…

A thin incompressible neo-Hookean sheet of undeformed thickness

H_0=1.35\,\mathrm{mm}

occupies the reference…

An incompressible Mooney–Rivlin continuum with

W=C_{10}(I_1-3)+C_{01}(I_2-3)

,

C_{10}=102\,\mathrm{kPa}

…

An incompressible neo-Hookean tensile bar has stored energy

W=(\mu/2)(I_1-3)

,

\mu=226\,\mathrm{kPa}

, and…