Solutions for analytical models of systems with nonlinear constraints have focused on exact methods for satisfying the constraint conditions. Exact methods often require that the constraint can be expressed in a piecewise-linear manner, and result in a series of mapping equations from one linear regime of the constraint to the next. Due to the complexity of these methods, exact methods are often limited to analyzing a small number of constraints for practical reasons. This paper proposes a new method for analyzing continuous systems with arbitrary nonlinear constraints by approximately satisfying the constraint conditions. Instead of dividing the constraints into multiple linear regimes, a discontinuous basis function is used to supplement the system’s linear basis functions. As a result, precise contact times are not needed, enabling this method to be more computationally efficient than exact methods. While the discontinuous basis functions are continuous in displacement, their derivatives contain discontinuities that allow for the nonlinear forces to be accounted for with the assumption that the nonlinear constraints are able to be modeled in a discrete manner. Since each nonlinear constraint requires only one associated discontinuous basis function, this method is easily expanded to handle large numbers of constraints. In order to illustrate the application of this method, an example with a pinned-pinned beam is presented.

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