Study On Multi-size And Contact Problems Of Continuum Structures Based On Discrete Solid-element Method

The discrete solid-element method is a new method applicable to the strongly nonlinear simulation of continuum structures,which has unique advantages in dealing with complex mechanical behaviors including large deformation,material nonlinearity,fracture and contact problems.In the physical model of the discrete solid-element method,there is only one radius of the spherical element.In order to obtain a high-precision model,it is necessary to use spherical elements with the smaller radius,which would result in a large amount of calculation and low computational efficiency.When structures have a large deformation,the contact may occur between different members or between the members themselves.Ignoring the contact behavior of structures would seriously affect the calculation accuracy and even lead to errors.Based on the discrete solid-element method,a multi-size connection model that can connect different radius spherical elements is proposed,and the contact calculation method applicable to discrete solid-element method is established to realize the refined analysis of continuum structures.The mechanical behaviors such as large deformation,material nonlinearity fracture and contact of continuum structure are studied.The main contents are as follows.(1)The basic theory of the discrete solid-element method is elaborated,and the spring stiffness considering the boundary effect is redetermined from the perspective of the basic cube.Based on the principle of energy conservation,the distortion energy density coefficient is rederived.The initial yield function expressed by using the contact internal force is established by introducing the distortion energy density yield criterion.Based on the subsequent yield functions,the plastic scaling factors of ideal elastoplastic materials and bilinear isotropic reinforced elastoplastic materials are derived,and the elastic-plastic constitutive models are established.It is shown that the discrete solid-element method described in this paper is more accurate than the existing method in the elastic and elastoplastic analysis.(2)Based on the physical model of the discrete solid-element method,a multi-size connection model based on force transfer is proposed,which can connect two kinds of radius spherical elements.The relationship between the masses of the spherical elements and the spring stiffness in the region of large spherical elements,the region of small spherical elements and the transition region and those of the basic cube is established.Based on the principle of energy conservation,the spring stiffness in the basic cube of transition region is derived.A preprocessing module of the multi-size connection model is developed.The influence of the force transmission path,the inhomogeneous force caused by transition region and the relative size of regions of large and small spherical elements on the calculation results has been discussed.(3)The elastoplastic calculation method of a multi-size connection model based on force transfer is established.According to the principle of energy conservation,the distortional energy density coefficients in the basic cube of the transition region are derived.The correctness of the multi-size connection model based on force transfer is verified,and the capability in dealing with large deformation and strong material nonlinearity is demonstrated.(4)In order to overcome the limitations of the multi-size connection model based on force transfer,a multi-size connection model based on displacement transfer is proposed.According to the characteristics of spherical element arrangement in the discrete solid-element method,the methods to determine spherical elements with relationship of coupled displacement and couple displacement of spherical elements is proposed.The correctness of multi-size connection model based on displacement transfer is verified,and the calculation results of the multi-size connection models based on force and displacement transfers are compared.The elasto-plastic and large deformation problem of the lap joint plate and the dynamic fracture problem of the single-lap glued joint are investigated.(5)According to the characteristics of the continuum and discrete solid-element methods,the contact theory applicable to the discrete solid-element method for the continuum structure is proposed.A subroutine for contact calculation is developed.The bucket sorting algorithm is used for global search to determine the potential contact pairs in the calculation space.The point-surface algorithm is used for local search to accurately determine the contact state of potential contact pairs.The normal and tangential contact forces are calculated according to the penalty function method.The full process simulations of centered collision of elastic rods,square block sliding considering friction,square block impacting cantilever beam and impact test of a grid shell are carried out to verify the correctness of the contact theory and subroutine of the discrete solid-element method.The theoretical analysis and numerical examples show that the discrete solid-element method is feasible and effective in analyzing strong nonlinear mechanical behaviors such as large deformation,material nonlinearity,fracture and contact of continuum structures.The multi-size connection model proposed in this paper can balance the accuracy and efficiency,which can guarantee the accuracy and improve computational efficiency at the same time.It is very suitable for complex structures with large local deformation or local damage,and provides a new technical means for the computation of strong nonlinear mechanics of continuum structures.