We present several preconditioned conjugate gradient methods for the iterative solution of the linear, symmetric systems of equations arising from the finite element method in displacement form, both for the h-version and the p-version. The preconditioners are based on a decomposition of the solution spaces into overlapping subspaces and solving separately on each subspace. A judicious choice of the subspaces gives good convergence for a uniform mesh. Local adaptive techniques are employed to modify the subspaces for real-world problems with distorted meshes and thin 3D elements. Computational results on workstations are presented for solid and shell aircraft structures and up to over 1,000,000 degrees of freedom and 4GB stiffness matrix.