Geometry

Basic construction elements are simple geometry types, that are used for shape definition of structural members and geometrical object. With defining the further attributes to these elements from the lists Structural analysis elements, Supports and hinges and Loads the complete structural model is created. All values refer to the list StrucutralPointConnection.

Following geometrical types are available:

Geometry type

Type definition

Insertion data explanation

SAF geometry strings

Notes

Mathematical definitions:

Bezier $Q(t)=\sum_{i=0}^{3}P_iB_i(t)$ ; $t\epsilon<0,1>$ $B_{0t}=(1-t)^3,B_{1t}=3t(1-t)^2,B_{2t}=3t^2(1-t),B_{3t}=t^3$ $Q(t)$ is for the Bezier curve $P_{i}$ is for coodinates, and $B_{it}$ is for basis function
Spline $Q(t)=\sum_{i=0}^{m}P_iN_i^n(t)$ ; $t\epsilon<t_i,t_{i+1}>$ $N_i^0(t)=1$ for $t\epsilon<t_i,t_{i+1}>$ $N_i^0(t)=0$ otherwise $N{i}^{k}{(t)}=\frac{t-t_i}{t_{i+k}-t_i}N_{i}^{k-1}{(t)}+\frac{t_{i+k+1}-t}{t_{i+k+1}-t_{i+1}}N_{i+1}^{k-1}{(t)}$ $Q(t)$ is for the Spline curve $P_i$ is for the coordinates $N_i^n(t)$ is for basis function $n$ is for the degree of curve $m$ is for points of the control polygon

Polyline schematics:

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