Verification Examples

A thin-walled conical vessel is filled with water. Thus, it is loaded by the hydrostatic pressure. While neglecting self-weight, determine the stresses in surface line and circumferential direction. The analytical solution is based on the theory of thin-walled vessels. This theory was introduced in Verification Example 0084.

The mathematical pendulum consists of a zero‑weight rope and a mass point at its end. The pendulum is initially deflected. Determine the angle of the rope at given test time.

Closely coiled helical spring is loaded by a compression force. The spring has a middle diameter D, the wire diameter d, and it consists of i turns. The total length of the spring is L. Determine the total deflection of the spring for the member model and one‑turn deflection for the solid model.

A cable in the initial position is loaded by two concentrated forces. The self‑weight is neglected. Determine the normal forces in the cable.

A shell roof structure under pressure load is modelled, where the straight edges are free, while at the curved edges the y- and z‑translations are constrained. Neglecting self‑weight, compute the maximal (absolute) vertical deflection, and compare the results with COMSOL Multiphysics 4.3.

Pinned beam with rectangular cross‑section is subjected to distributed loading and shifted vertically by eccentricity. Considering small deformation theory, neglecting self‑weight, and assuming that the beam is made of isotropic elastic material, determine the maximum deflection.

A thin-walled spherical vessel is loaded by inner pressure. While neglecting self‑weight, determine the von Mises stressand the radial deflection of the vessel.

A thin string is tensioned by the initial strain and initially deflected. Determine the deflection of the test point at given test times.

A double-mass oscillator consists of two linear springs and masses, which are concentrated at the nodes. The self-weight of the springs is neglected. Determine the natural frequencies of the system.

A simple oscillator consists of mass m (considered only in x-direction) and linear spring of stiffness k. The mass is embedded on a surface with Coulomb friction and is loaded by constant-in-time axial and transversal forces.

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