When generating a conformal mesh for Finite Element Analysis (FEA), careful attention is required to ensure that the nodes along an interface exactly match each other. This is true when various components are meshed independently. But even if the structure is meshed as a whole, there still may be components with an undesirable mesh resolution. Time and computing power are wasted by iterating through different mesh configurations until an acceptable one is found. To overcome these issues, it would be better to mesh each component independently of the others. Tie constraints are utilized to connect these non-conformal meshes. This research assesses how the implementation of tie constraints affects the accuracy, robustness, and efficiency of solving FEA problems in two-dimensions. To accomplish this, a finite element code, PRoFile, is written in C. A static structural analysis is performed on three types of beams: one in axial tension, one cantilever, and one simply supported. With meshes of varying resolution, each configuration is run through PRoFile and compared to the solution found when no ties are used. It is shown that, if implemented properly, the tying schemes have little negative impact on the accuracy of the solution but increase the time required to obtain a solution from PRoFile. The results from this investigation will be useful for the analysis of aircraft designs involving components from multiple parties. Typically, all components of the aircraft must be gathered and meshed together. It would be easier if each party were to make a mesh for their respective aircraft components and then tie all of the meshes together before the structure undergoes FEA. That way, if one component is re-designed, the entire aircraft does not need to be re-meshed-only the single component is re-meshed and the ties to the other components on the aircraft are updated.