•Functionally graded materials (FGM) beams under bilateral constraints•Experimental testing and theoretical and numerical validations•Systemic study on the influences of geometric and material parameters•Material topology for optimization of material functions In recent years, the study of Functionally graded materials (FGM) opened exciting new venues for the control and manipulation of engineered materials and structures. In this study, we investigate bilaterally constrained FGM beams with programmable material functions. The FGM beams are fabricated using 3D printing techniques, and tested t understand the behavior of structural instability (i.e., postbuckling) under the bilateral confinements. Theoretical and numerical models are developed to investigate the postbuckling response, and the results are compared to experimental observations with satisfactory agreements. Material topology optimization is then carried out to investigate the influences of the material functions on the release of the stored energy during the bucking mode transitions in the FGM beams. It is found that stored energy variations can be used to optimize the material functions, which allows for the guided design of bi-walled FGM beams with well-defined controllability over the structural instability. The reported bilaterally constrained FGM beams with optimized material functions can be used in a multitud of different applications. Display omitted