<p>This study develops a novel, data-driven family of through-thickness shape functions for higher-order shear theories of laminated plates and, more broadly, introduces an optimization-based methodology for constructing kinematic assumptions in structural mechanics. Each function combines a cosine-exponential kernel with an even-order polynomial whose coefficients are identified by an extended K-means clustering procedure, so that the resulting transverse-shear distribution is optimally fitted to exact three-dimensional elasticity solutions. Because the kernel-polynomial product has no closed-form antiderivative, all thickness integrals needed for stiffness and mass matrices are evaluated by the composite trapezoidal rule, making the approach easy to embed in existing finite-element or isogeometric codes. The higher-order formulation is implemented in an IGA framework with NURBS basis functions, ensuring exact geometry and the continuity requirements of the new series. Its accuracy is demonstrated through static bending and free-vibration analyses of simply supported laminated plates under sinusoidal and uniform loads, where mid-plane deflections, in-plane stresses, interlaminar shear stresses, and natural frequencies are benchmarked against recent kernel-based models and three-dimensional elasticity. The proposed shear-deformation functions consistently yield closer agreement at comparable computational cost. More importantly, the optimization-driven construction provides a systematic and generalizable strategy for designing through-thickness shape functions, offering a new scientific basis that can be extended to other plate and shell theories and to a wider class of mechanics problems.</p>