Questions tagged [solid-mechanics]
Solid mechanics deals with the solid bodies subjected to various type of loading and internal forces generated due to this loading.
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Calculating the bending moment ($M$) of a beam as it relates to stress ($σ$) and strain ($ε$)?
I am trying to learn how to work out the bending moment for progressively complex systems to model a beam. I am assuming only one axis of motion (transverse = $y$).
For the basic equation of material ...
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Is there any formula to model the effective Young's Modulus of a fluid-filled spherical shell?
I am creating composites of a host epoxy and filler particles which are thin-walled fluid-filled shells. Using the Halpin-Tsai equations, for example, I can predict the bulk composite Young's modulus ...
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I don't understand a simulation result of frequency vibration analysis of ultrasonic tranducer
I am building a ultrasonic transducer like this (with double-exponential (75%-25%) match and 2 ring PZT8 50x20x6.5 (for the moment I do not take account of pre-stress on bolt) :
When I simulate the 2 ...
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Glass bottle with a prolonged neck that continues into the inner space
Is it possible to create following two shapes from glass using currently known glass mass production techniques?
Shape #1: bottle with a prolonged neck that continues into the inner space, like this (...
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How is motor torque related to capstan equation?
I know that capstan equation relates $T_{in}$ and $T_{out}$ as $T_{out} = T_{in}e^{u \cdot F_c}$, where $u$ is friction coefficient and $F_c$ is wrap (slip) angle. In my situation, the capstan is ...
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Column Buckling Boundary Conditions -- Welded Tubing Practical Application?
I'm trying to do some calculations for a personal project. I'm trying to understand column strength / buckling. My questions relate to Effective Length Constant, which is based on Boundary ...
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Thermal Expansion and Stress in a Heated Beam
Consider the case of a beam that is supported in such a way that expansion can occur freely. Suppose that the beam is heated in such a way that the temperature varies with the depth of the beam. Let $...
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Magnetic Force - Point of Load
I am using a Magnet like this in an assembly and I am trying to calculate the torque in point P2 (see picture below) resulting from the attraction force F between my magnet and the steel part.
As I ...
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Finding the Shear Center for a Beam with 1 Axis of Symmetry
I am trying to solve this problem of finding the shear center for the given beam and I have found that e = 35.94 mm, however the solution that was shared with me, had the answer of 39.17 mm.
My method ...
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Why the variable "r" appears in circumferential force balance for a membrane
I am trying to understand a force balance for an inflating membrane (reference cited at the bottom of the post) and can't figure out why there is an "r" in the circumferential balance.
The ...
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Deformation gradient tensor from particle displacements in an inflating material
I don't have a mechanics background, but am trying very hard to read and understand how to approach this problem. I am struggling with understanding what's "correct" or the basic process of going from ...
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Determinating Reactions for the following frame
According to the frame below, the goal is to determine the reactions of this frame in order to draw after the diagrams N, T and M.
The frame is asymmetric by reference at point C.
All reactions ...
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What is the meaning of the traction continuity condition in the generalized momentum balance (continuum mechanics)?
In Nonlinear Finite Elements for Continua and Structures by Belytschko and al. it is stated:
As we have already noted, the strong form, or generalized momentum balance, consists of the momentum ...
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Problems in the application of the first theorem of Castigliano for a cantilever beam
I'm having contradictory results while applying the first theorem of Castigliano for the cantilever beam shown in the figure above. Due to P and the restrictions on point $B$, it will have a bending ...
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Why is there a negative sign in case of moments caused by longitudinal stresses?
I came across the following relations in the plate theory. I, however, don’t understand the reason for the negative signs in Mx and My. There is, however, no negative sign in Mxy. I am guessing, this ...
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how to determine the direction of support reactions in a truss?
Hi, I am not sure how to determine the direction of support reactions at point A and K. I know point A has a pin support, therefore, it can take in horizontal and vertical loads and point K has a ...
user38335
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Bending stress wave resulting from a lateral impact on a beam
I want to approximate a bending stress wave resulting from a lateral impact on a beam which is on one end fixed.
According to Roarks 16.3-3 I can estimate a compressive stress wave from one mass ...
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Strain gauge measurement using NI 9944
I am trying to measure the strain on a part using a strain gauge. The gauge is a 120 $\Omega$ strain gauge from HBM. I am using National Instruments (NI) hardware and LabVIEW software to capture the ...
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Does numerical dissipation in FE simulations affect system's elastic energy? Does it depend on thickness?
I am running a finite-element simulation in Abaqus, for which I also have a theoretical model. To be precise, I am simulating wrinkling in a thin annular sheet, with shell elements. The model makes a ...
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Why doesn't the Stress Power in the theorem of the expended mechanical power contribute to the kinetic energy?
The following is the formula of the expended mechanical power:
$P(t)$ $=$ $\frac{d}{dt}$ $\int \frac{1}{2} \rho\ v^2 dV$ $+$ $\int \sigma \colon d\ dV$
where $P(t)$ is the mechanical power entering ...
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Definition of Mass in Multiple Mass Oscillators
In an exam on seismics and earthquake proof design I had a couple of days ago, there was a question on multiple mass oscillators in the form of a simply supported beam of length $L$, stiffness $EI$ ...
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Linear FEM: Infinitesima Strain tensor at different element mesh
Hi guys,
I am solving an exercise for a course of Computational Continuum Mechanics. Briefly, my question is how can i compute the infinitesimal strain tensor at different nodes of the finite element ...
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How is the slip calculated in Abaqus small-sliding interaction?
I’m doing research on the sliding of 2 fracture surfaces.
To do that, I’m trying to understand the Small-sliding deformable interaction in the Abaqus (2018), and I use the Node-to-surface ...
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Plastic Multiplier for Perfectly Plastic Materials
I'm trying to apply the associated flow rule to elastic-perfectly plastic material,
i.e.,$$d\epsilon_{ij}^p=\lambda\dfrac{\partial f}{\partial \sigma_{ij}}$$,
where $f$ is a yield function with no ...
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3
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535
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Honeycomb structures vs shear stress
Honeycomb structures are made of top and bottom shells and honeycomb geometry at core. In terms of bending load, maximun normal strains take place on top and bottom hence, sheet parts can support them ...
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Is it possible to change a 'relaxing length' of edges for 8 node hexaedral element in 3d FEM
I am using 3D FEM with 8 node brick element to model a certain type of growth/expansion, which is not a plastic deformation. First, I apply a pressure/load and I get displacement and new position of ...
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What is the difference between maximum principal strain and maximum in-plane principal strain?
For the purpose of answering/explaining this, it does not need to be restricted to strains (i.e., it can be stresses too). I am mainly trying to understand when to use which one (i.e., if I am ...
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Rationale For Plain Strain Assumption in Long or Infinite Bars
When plane strain is discussed, there are two examples given, both of which involve two dimensional boundary stress conditions. One is a constrained object that cannot move along the third axis. From ...
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Vertically oriented shaft sleeve rubbing against bearing - Calculating side load due to a certain amount of tilt
At some given angle of tilt, we will perceive the pressing of a rotating SS shaft sleeve against a greased bronze journal bearing. How would you compute the side load force on the bottommost bearing ...
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Specific Heat, Pore Fluid In ABAQUS
I want to model a problem that the theory behind is in the "Coupled Pore Fluid Flow and Stress Analysis" context that there is in the ABAQUS online documentation, version 2022. The link to ...
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Mechanics of Materials Method for Curved Beam with Different Centers
The common curved beam theory covered is the Winkler method (e.g. in Johnston and Beer, or Boresi and Schmidt). As can be seen by reading any derivation, this method applies to beams with a common ...
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Error while using VWRITE command in ANSYS APDL
I am writing code in APDL for a nonlinear structural analysis of a plate.
Following is the Post processing part which returns a formatting error. Help will be appreciated in identifying the problem ...
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Moment at the end of the shaft, after a bearing?
I have an application with an interchangeable load. That can be swapped in a machine.
The bearing and break are both mounted to different sides of the same plate
The load is placed on two shafts that ...
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Building Equations of Motion
The following figures represent a model of a building, can someone help me, extract the newton equations of motion and determine the degrees of freedom.
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Plane strain delamination on bilayer material (conversion from material stress state to residual force and moment)
I have been reading the book The Mechanics and Reliability of Films, Multilayers and Coatings (https://doi.org/10.1017/9781316443606) on chapter 4.2 and got stuck in chapter 4.2 and 4.3.
Suppose that ...
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Which design is most resistant to tipping against 90 degree downward force?
Have a question sort of related to question at (What calculation to find how much force before tipping over?) but with slight modifications.
Trying to weld some tubing together and onto a heavier base ...
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Why are the indices of term of the Cauchy Stress Tensor and Maxwell Stress Tensor opposite to each other?
For CST (https://en.wikipedia.org/wiki/Cauchy_stress_tensor), the first index represents the plane and the second index represents the direction:
For MST (https://en.wikipedia.org/wiki/...
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Why is there a lack of data and analysis of elastic range of PTFE (Teflon)?
I am looking for the proportionality limit and elastic limit of PTFE (Teflon).
There are several papers which reported the mechanical behavior of PTFE in tensile test. However, almost all of those ...
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CNC a hemisphere in SolidWorks
Dear all, I am currently learning CNC Milling software. I have successfully be able to simulate the toolpath for milling a square block to a hemisphere. May I ask how to add another operation, that is ...
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Why carrom coins have the circular profiles on them?
Why do carrom coins have these circular profiles on them? At first I thought that this will reduce the friction as area reduces, but quickly recalled that friction for solids don't really depend that ...
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How can I recover the deformation gradient from the finite element strain result
I have performed a finite element simulation which corresponds to the example in https://de.wikipedia.org/wiki/Deformationsgradient#Beispiel .
The result from the theory in wikipedia is the following (...
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Using Strain Tensors to Recover Stress Tensors
Disclaimer:
I am very new to the field of mechanics, my background is in electrical engineering. I apologize in advance if anything is horribly wrong.
My references are:
"First Course in FEM, 4th ...
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Is the a similar method of calculating moment in inelastic bending like in the case of torque for inelastic torsion?
When calculating for Torque in torsion or for Moment in the case of bending, the concept is usually first introduced with the simplification of the assumption that the stresses and strains are in the ...
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How to determine the flexibility coefficent of this six member truss using the unit-load method?
I'm studying the Flexibility method described in the book "Matrix analysis of framed structures" by James M. Gere but I'm having a hard time understanding one of the examples. I'm stuck at ...
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Investigation of Body Motion in SolidWorks: Euler Angles Rate or Angular Velocity?
This is my first question in this community.
I decided to demonstrate my problem on simple rigid body, but task may be applied to more complex shapes. So, a cube is built in SolidWorks:
Using the ...
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How to calculate Strain Energy Density from Abaqus hyperelastic simulation?
I am modeling a deformation of a rubber material using Abaqus/Explicit using Ogden hyperelastic model. I can visualize Stress (S) and Displacements (U), but I am interested in plotting the strain ...
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Finding the bending moment diagram for an indeterminate continuous beam
In a recent lecture, we had the following example of an indeterminate continuous beam where we must find the redundant support reaction at $A$:
This was found by removing the support at $A$, and then ...
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Which CNC gantry support shape is more ridgid?
I'm in the process of designing a small CNC. There are two styles of side plates for supporting the gantry. The first one has an angled corner cut on the front, while the other has a backslash shape. ...
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Fixed Free Fixed Free Rectangular Plate Subjected to a Point Load solved by FDM
The equation for deflection of a rectangular plate by using classical plate theory is given as,
Here Pz value on the RHS is uniformly distributed load acting on entire plate in Newton per metres.
...
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stress power of a solid
In the balance of mechanical energy https://pkel015.connect.amazon.auckland.ac.nz/SolidMechanicsBooks/Part_III/Chapter_3_Stress_Mass_Momentum/Stress_Balance_Principles_08_Cons_of_Mech_Energy.pdf,
$\...
