<p>Helicoidal schemes and designs in biological composite constructions enable them to absorb high-impact energy with amazing efficiency and offer exceptional resistance against damage. However, little research has been done on how reorienting and redirecting fibers inside a helicoid structure’s matrix affects the structure’s response and mechanical performance. This study is innovative in that it uses isogeometric analysis in conjunction with modified first-order strain theory to examine the forced and free oscillation response of a doubly curved shallow shell made of bio-inspired helicoid laminated composite (B-iHLC) under low-velocity impact load in a hygro-thermal environment. The B-iHLC shallow shell lying on a visco-Pasternak medium is defined by two stiffness coefficients and one damping coefficient. In this article, the impact load model is described analytically using a single spring-mass model. The equilibrium equations of the shell are derived based on Hamilton’s Principle, and then Newmark’s direct integration approach is used to derive the transient responses of the B-iHLC shell and load during the collision. A series of numerical comparisons with reputable publications is performed to assess the accuracy of the model and the article’s calculation technique. The validity of the article’s model and methodology is verified by conducting numerical comparisons with well-regarded publications. These discoveries may be used in the building of civil works and military applications when the shell is exposed to extreme forces.</p>