[ [K(u)]u = F(u) ]
At iteration (i), ([K_T^i]) is the tangent stiffness matrix, (F_int^i) the internal force vector. The solution update is:
Newton-Raphson diverged when stiffness became negative. Displacement DOF at crown exceeded 1e7 mm. ansys an internal solution magnitude limit was exceeded
where ([K]) is the stiffness matrix (dependent on displacement (u) in nonlinear cases), (u) the displacement vector, and (F) the applied load. The Newton-Raphson method iteratively solves:
[ u^i+1 = u^i + \Delta u^i ]
Abstract: The error “An internal solution magnitude limit was exceeded” is a fatal termination code encountered during nonlinear finite element analysis (FEA) in ANSYS. It indicates that a computed degree of freedom (DOF) value—typically displacement, rotation, temperature, or voltage—has surpassed an internal threshold (default (10^7) in many units). This paper dissects the mathematical origins of the error, links it to numerical instability in the Newton-Raphson solution scheme, and provides a hierarchical diagnostic framework. Primary causes include rigid body motion, unstable buckling, material instability, mesh distortion, and poorly conditioned contact. Mitigation strategies range from model verification to advanced solver controls (e.g., arc-length method, line search, stabilization). 1. Introduction In implicit FEA, the global system of equations is:
where (R) is the residual force vector. As ( \lambda_\min ) approaches zero, even a tiny residual yields enormous displacement increments—triggering the error. [ [K(u)]u = F(u) ] At iteration (i),
[ [K_T^i]\Delta u^i = F_ext - F_int^i ]