Dynamic relaxation is a method commonly used for form finding of shell structures. It was introduced by Alistair Day  and solves the nodal position for each node in the structure in such a way that nodal equilibrium is fulfilled
in which is the sum of all the applied external loads and the support reaction if the node is restrained, and the internal force in member ending in node .
As long as the position is incorrect a out of balance or residual force appears at each node
By introducing a small time step and a fictitious mass at each node, we can trace the structure’s (fictitious) motion in time as it moves towards the equilibrium position.
To update the position for node , the following three operations are performed consecutively
where and are the acceleration and velocity of the node, respectively, and is a damping parameter introduced to ensure numerical stability.
The mass is fictitious and adjusted to adjusted to optimise the rate of convergence  and usually taken as
where is the largest direct stiffness occuring at the node during the simulation. Further strategies on choosing the fictitious mass is discussed in , including using different masses in different directions, effectively turning the mass in to a vector .
If there only exists axial stiffness in the system, the internal force in member is found from
where and are the tension in member and the current length, respectively. is a unit vector in the direction from node to node .
It should be noted that so far we have discussed pure static equilibrium. No assumptions have been made regarding the material properties of the members which might be linear or non-linear elastic or be subject to creep or plastic deformation. The structure may be statically determinate or indeterminate or even a mechanism, provided that it is in equilibrium. The structure may have undergone a large deformation from some initial state.
In order to determine the form found geometry we need further information regarding the tensions and their relationship with the current lengths . The simplest relationship is linear elastic,
in the case of a member with unstressed length . The constant in which is equal to the Young’s modulus times the cross-sectional area of the member. However, during form finding we can postulate any relationship between tension and length, including inextensible members whose length cannot change and members with a constant tension.
 A. S. Day. An introduction to dynamic relaxation. The Engineer, 219:218–221, 1965.
 M. R. Barnes, “Form finding and analysis of tension structures by dynamic relaxation,” International Journal of Space Structures, vol. 14, no. 2, pp. 89–104, 1999.
 M. Rezaiee-pajand, M. Kadkhodayan, J. Alamatian, and L. Zhang. A new method of fictitious viscous damping determination for the dynamic relaxation method. Computers & Structures, 89 (9–10):783–794, 2011.