验算示例

Helicoid

A membrane is stretched by means of isotropic prestress between two radii of two concentric cylinders not lying in a plane parallel to the vertical axis. Find the final minimal shape of the membrane - the so-called helicoid, and determine the surface area of the resulting membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

Catenoid

A cylindrical membrane is stretched by means of isotropic prestress. Find the final minimal shape of the membrane - catenoid. Determine the maximum radial deflection of the membrane. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

Cable Equilibrium Force

A cable is loaded by means of the uniform load. This causes the deformed shape in the form of the circular segment. Determine the equilibrium force of the cable to obtain the given sag of the cable. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, also self-weight is neglected in this example.

Balloon – Prestressed Membrane

A spherical balloon membrane is filled with gas with atmospheric pressure and defined volume (these values are used for FE model definition only). Determine the overpressure inside the balloon due to the given isotropic membrane prestress. The add-on module RF-FORM-FINDING is used for this purpose. Elastic deformations are neglected both in RF-FORM-FINDING and in analytical solution, self-weight is also neglected in this example.

Catenary

A very stiff cable is suspended between two supports. Determine the equilibrium shape of the cable, the so-called catenary, consider the gravitational acceleration and neglect the stiffness of the cable. Verify the position of the cable at given test points.

Cable with Concentrated Forces

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

Mathematical Pendulum

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.

Free Vibrations of String

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

Geometric Non-Linearity of Member with Spring

Slightly sloped member is loaded with the force and held by spring at one end and supported at the other and. Assuming large deformations and neglecting member's self-weight, determine its maximum upward deflection.

Cantilever with the Moment Loading at the Free End

A cantilever is loaded by the moment at its free end. Using the geometrically linear analysis and the large deformation analysis and neglecting beam's self-weight, determine the maximum deflections at the free end.

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