Nonlinear Finite Element Analysis Of Beam And Shell Structures Based On SiPESC

Curved shell structures can carry normal loads through in-plane deformation(membrane force)and make full use of material properties,so shell structures have been widely used in many engineering fields,such as aerospace,pressure vessels,large construction and so on.This kind of structures are made up of many slender,thin-walled structural components,the deformation of them is usually characterized by large rotations and small strain.Buckling and unstability are the main forms of shell structures failure,so they usually need to be reinforced with ribs to improve their bearing capacity.So we need to apply geometrically nonlinear finite element analysis to them.Modelling these structures with beam elements,shell elements or their combination can greatly reduce the solution scale of the problem.SIPESC,an independently developed software integration platform for engineering and scientific computation,have constructed universal implicit nonlinear finite element solution framework,but this framework doesn’t provide nonlinear beam element and shell element.This limits the analytical capability of the framework.In order to make SiPESC have the ability of geometrically nonlinear analysis for beam and shell structures,this paper firstly studies the theory of nonlinear beam and shell element and derives the formulations of them in detail.Furthermore this paper develops three kinds of elements on SiPESC,namely geometrically exact beam,degenerated shell and stress resultant shell with drill rotations.Their characteristics as follow:Geometrically exact beam describes its rotation by an orthogonal rotation tensor fixed on its cross-section.Without any numerical approximate in its rotation update process,so it can exactly calculate any large three dimentional finite rotations.Degenerated shell can get rid of locking by using enhanced assumed strain method(EAS)and assumed natural strain method(ANS).Dropping components of the incremental rotations axial vector along the thickness direction make the element get rid of the singularity caused by absence of in-plane rotational stiffness.Stress resultant shell with drill rotations is suitable for the analysis non-smooth shell structures.At the same time,the rotation description of this element is the same as the geometrically exact beam.So this kind of shell element can be used with geometrically exact beam element for the analysis of beam and shell combination structures.Direction of nodal force of structures may depend on structural deformation.For example,the load of aircraft provided by panel method when performing aeroelastic analysis of it.This paper proposes a strategy to handle this kind of load:defining an orthogonal rotation tensor on the node and updating it with incremental rotational displacement to determine the drection of the nodal force after deformation.This method can be used to analysis of the load of any nonlinear beam and shell element that describe it’s rotation by an orthogonal rotation tensor.And external force stiffness related to this load is deduced,in order to improve the convergence of the solution.A series of Benchmarks example are used to verify the performance of these elements,the solution is the same as the theoretical solutions.It show this paper can get correct result.Finally,this paper conducts a numerical examples for engineering problems,a wing model made up of beam elements,and get the same results as ANSYS.It proves that SiPESC can perform geometrically nonlinear analysis of beam and shell element for practical structures.