Static And Dynamic Analysis Of The Curved Compliant Mechanism Based On IGA

Compliant mechanism is widely used in the advanced fields such as precision engineering,bionic machinery,biomedicine,and aerospace due to its simple structure,freedom from friction and wear,ease of energy storage and transformation,and adaptability to complex and harsh environments.New application areas put new demands on the working space and various performance indicators of flexible mechanisms.The traditional straight beam structure analysis is simple,but the geometric parameters are few,the adjustment range is limited and the stress concentration is easy to occur in the case of large deformation,and accelerate the structural fatigue failure.Curved compliant units can be widely used to avoid the above situations.Conventional finite element analysis is difficult to directly analyze arbitrary curved beams affected by curvature.In this paper,we research the statics,dynamics and geometric nonlinearity of general arbitrary curved beams based on IGA.According to the principle of Non-Uniform Rational B-Spline,complete the geometric construction of the general planar curved beam model.Based on IGA,combined with the principle of minimum potential energy,complete the statics and dynamics analysis of general arbitrary curved beam model,give the display integral expressions of stiffness matrix and mass matrix described by NURBS basis functions.The whole solution process is realized by MATLAB programming using Gauss integral method.The accuracy of the procedure is verified by numerical examples,at the same time,the relationship between the performance indicators of the static beam displacement and dynamic natural frequency of the curved beam model and the control point weight factor is revealed.After obtaining the linear stiffness matrix and mass matrix of a general arbitrary curved beam based on IGA,further analysis is carried out under the condition of large deformation and nonlinearity.First,give the general geometric nonlinear description process,and deduce the general expression of large deformation tangent stiffness matrix,then combine the mechanical equations of any curved beam model,derive the tangent stiffness matrix of arbitrary curved beam under geometric nonlinearity based on IGA.Introduce the general numerical solutions of several common nonlinear equations.The accuracy of the tangent stiffness matrix obtained is verified by the load increment method combined with two curved beam examples.According to the configuration method of degree of freedom and constrained topology,combined with the principle of NURBS spline configuration,a three-degree-of-freedom planar curved beam compliant mechanism was designed.Mechanical analysis of the overall structure based on IGA in MATLAB to determine the various performance indicators of the organization.According to the kinematic equivalence principle,several sets of compliant mechanisms with the same degree of freedom but different shapes and performance indexes are obtained by adjusting the control points and weight factors without changing the parameters such as elastic modulus and cross-sectional area of the beam elements.It provides another idea for subsequent design,analysis and optimization of compliant mechanisms of arbitrary curved beams.