A C 0 conforming dg finite element method for biharmonic equations on triangle/tetrahedron

A C 0 conforming discontinuous Galerkin (CDG) finite element method is introduced for solving the biharmonic equation. The first strong gradient of C 0 finite element functions is a vector of discontinuous piecewise polynomials. The second gradient is the weak gradient of discontinuous piecewise polynomials. This method, by its name, uses nonconforming (non C 1) approximations and keeps simple formulation of conforming finite element methods without any stabilizers. Optimal order error estimates in both a discrete H 2 norm and the L 2 norm are established for the corresponding finite element solutions. Numerical results are presented to confirm the theory of convergence.

Parameter identification of a second-gradient model for the description of pantographic structures in dynamic regime

Pantographic structures are examples of metamaterials with such a microstructure that higher-gradient terms’ role is increased in the mechanical response. In this work, we aim for validating parameters of a reduced-order model for a pantographic structure. Experimental tests are carried out by applying forced oscillation to 3D-printed specimens for a range of frequencies. A second-gradient coarse-grained nonlinear model is utilized for obtaining a homogenized 2D description of the pantographic structure. By inverse analysis and through an automatized optimization algorithm, the parameters of the model are identified for the corresponding pantographic structure. By comparing the displacement plots, the performance of the model and the identified parameters are assessed for dynamic regime. Qualitative and quantitative analyses for different frequency ranges are performed. A good agreement is present far away from the eigenfrequencies. The discrepancies near the eigenfrequencies are a possible indication of the significance of higher-order inertia in the model.

Uniqueness theorem in coupled strain gradient elasticity with mixed boundary conditions

The equilibrium equations and the traction boundary conditions are evaluated on the basis of the condition of the stationarity of the Lagrangian for coupled strain gradient elasticity. The quadratic form of strain energy can be written as a function of the strain and the second gradient of displacement and contains a fourth-, a fifth- and a sixth-order stiffness tensor $${\mathbb {C}}_4$$ C 4 , $${\mathbb {C}}_5$$ C 5 and $${\mathbb {C}}_6$$ C 6 , respectively. Assuming invariance under rigid body motions the balance of linear and angular momentum is obtained. The uniqueness theorem (Kirchhoff) for the mixed boundary value problem is proved for the case of the coupled linear strain gradient elasticity (novel). To this end, the total potential energy is altered to be presented as an uncoupled quadratic form of the strain and the modified second gradient of displacement vector. Such a transformation leads to a decoupling of the equation of the potential energy density. The uniqueness of the solution is proved in the standard manner by considering the difference between two solutions.

A Preliminary Exploration of Landscape Preferences Based on Naturalness and Visual Openness for College Students With Different Moods

The interaction between man and nature causes people to have different preferences for their surrounding environment, and pleasant landscapes can bring both physical and mental benefits to people. Previous studies have demonstrated the relationship between moods and landscape preferences, and this study sought to explore the landscape preferences of college students under different moods. A total of 1,034 students participated in the survey, recovering 1,022 valid questionnaires. The Profile of Mood States (POMS) scale was used to evaluate the mental status of each respondent. The study on landscape characteristics proceeded in two steps (comprising four gradients): landscape naturalness and landscape visual openness. The research results show that under natural landscape conditions, college students in a fatigued state have a greater preference for the second-gradient (higher naturalness) landscape environment; under the conditions of landscape visual openness, college students in an indignant state have a greater preference for the second-gradient (relatively private) landscapes. These findings have significance for exploring the rehabilitation function of landscape architecture and have a guiding role for future landscape design.

On the statics and dynamics of granular-microstructured rods with higher order effects

Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts.