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The use of global displacement basis functions to solve boundary-valueproblems in linear elasticity is well established. No prior work uses a globalstress tensor basis for such solutions. We present two such methods for solvingstress problems in linear elasticity. In both methods, we split the soughtstress $\sigma$ into two parts, where neither part is required to satisfystrain compatibility. The first part, $\sigma_p$, is any stress in equilibriumwith the loading. The second part, $\sigma_h$, is a self-equilibrated stressfield on the unloaded body. In both methods, $\sigma_h$ is expanded usingtensor-valued global stress basis functions developed elsewhere. In the firstmethod, the coefficients in the expansion are found by minimizing the strainenergy based on the well-known complementary energy principle. For the secondmethod, which is restricted to planar homogeneous isotropic bodies, we showthat we merely need to minimize the squared $L^2$ norm of the trace of stress.For demonstration, we solve eight stress problems involving sharp corners,multiple-connectedness, non-zero net force and/or moment on an internal hole,body force, discontinuous surface traction, material inhomogeneity, andanisotropy. The first method presents a new application of a known principle.The second method presents a hitherto unreported principle, to the best of ourknowledge.

Solution of planar elastic stress problems using stress basis functions