Solid elements are used if a structure geometry, which is to be analyzed, cannot be described adequately by beam or area elements or if the ascertainment of the three-dimensional stresses is necessary for the evaluation of the structural behavior. Examples are the dynamic analysis of machine foundations or the calculation of concrete bridges with a complex geometry. The ability to model realistic support and connection conditions with contacts or nonlinear bedding also makes solid elements useful.

Modeling

Model objects are used to define a structure model. They consist of freely combinable partial solids that are created by the extrusion of sections or by entering polyhedrons with four to eight corners. Object properties like material, color, layer etc. can be assigned immediately. Bedding and contact properties can be defined at each model surface. Afterwards the complete solid model is meshed with tetrahedron elements taking into account all boundary conditions.

Modeling by extrusion

Entering polyhedrons

Assigning of surface properties

Solid model and completed tetrahedron mesh	8. Eigenmode

Loads

All necessary load types are available for the analysis of solid models:

• Dead load and nodal loads
• Free point, line and area loads
• Support displacement
• Linear temperature fields
• Free tendon layout / prestressing
• Creep and shrinkage
• Load model 1 for bridge construction
• Dynamic train load

Mode shape of a machine foundation

Analysis

For the FEM analysis a tetrahedron element with 10 nodes is available, which can exactly describe linear stress distributions and hence has a very good convergence of results. Also a high computation speed is associated with this element. Additionally to the static and dynamic abilities mentioned above stability analyses (second order theory, buckling, bulging etc.), contact elements and plastic material behavior (Huber - von Mises, Raghava) are implemented.

Dynamical contact problem of a beam model

After integration of the stresses with design objects, internal forces are available for the checks.

Head plate connection with contact conditions

Results

The possibilities of result preparation are important to evaluate the quality of a calculation. They are necessary to understand and document the structural behavior. Among others the following result representations are available for solid models:

• Deformation with animation
• Color surfaces
• Three-dimensional isosurfaces
• Surface sections
• Solid sections
• Principal stress vectors
• Integral internal forces for checks

The systems shown below give an impression of the various fields of application:

Prestressed, Precast Girders with In-situ Concrete

To analyze the bonding area between two precast girders, the solid model below was created with two construction stages. The precast girders were first calculated under dead load and prestressing. In the second construction stage, the in-situ slab and the cross girder were added. The supports were implemented from the prefabricated parts under the cross girder. The stress distribution shown below takes into account all external loads as well as the prestressing and redistributions from creep and shrinkage.