Study On Stress Hybrid Element Of Linear Elastic Dynamics

Structural dynamic analysis considering the inertial effect of loaded structures is becoming increasingly essential to meet the design requirements of engineering structures.The stress hybrid element method has been continuously developed since its introduction and has played an essential role in many science,technology,and engineering fields.Compared with the application in static analysis simulation,the research outcomes of the stress hybrid element method in the dynamic analysis simulation are somewhat thin.Some researchers used this method to address the problem of elastic dynamic vibration.They pointed out that the solution has the advantage of high approximation accuracy of field variables.Simultaneously,the solution process has the advantage of low sensitivity to mesh distortion and incompressibility or quasi-incompressibility.The Voronoi cell finite element method(VCFEM)based on the stress hybrid element method has the advantage that the divided Voronoi mesh diagram can accurately describe the size,shape,and spatial distribution randomness of the material microstructure and has become an effective means to solve the problem of complex composite materials,but dynamic analysis simulation only finds the application of one-dimensional problems。This paper studies the linear elastic dynamic stress hybrid element of twodimensional based on the above requirements and advantages.The main work is as follows:1.A new two-dimensional arbitrary polygonal stress hybrid dynamic element(APSHD element)is proposed for the dynamic response simulation of homogeneous materials.2.A new two-dimensional fluid-solid strong interaction stress hybrid dynamic element(FSSISHD element)based on the global integral strong coupling method,which can use for dynamic analysis of a fluid-solid coupling system,is constructed.3.For the APSHD element,an explicit polynomial form of the combined stress solution satisfying the motion equation in the element domain is given.Show the formula derivation process of the assumed form of the stress solution in detail,and form a process framework for constructing similar solutions.Write the numerical calculation program of the element in Fortran language,and the superiority of the element is verified.4.For the FSSISHD element,introduce new conditions,and derive new energy functional based on the APSHD element.Give the basic formula and finite element solution flow of the fluid-solid strong coupling stress hybrid dynamic element,and the element’s appropriate high-order stress solution form is discussed and explored.